Every Step Calculus

Show Work Step by Step on your TI-89 Calculator Screen

  • Home
  • Buy Now
  • Video Blog
  • Video List
  • Calculus Topics
    • Antiderivative Calculator
    • Derivatives
    • Integration by Parts
    • Simpsons Rule
    • U-Substitution
    • Vectors
  • Install
    • Mac Install
    • PC Install
  • Support
    • Troubleshooting for Install
    • Program Menu
    • Requirements
    • Controlling the Menu
    • Calculus Tips
    • Program Troubleshooting
  • Contact Me
    • Affiliate $
    • Tutoring
You are here: Home / Archives for Partial Fractions

Partial Fraction Example 7-Solved by TI-89 Video

September 19, 2014 by Tommy Leave a Comment

Raw Transcript

Hello Everyone, Tom from everystepcalculus.com and everystepphysics.com. Partial Fraction test problem. Index eight to get to my menu. Choose or school to Partial Fractions. I’m already there. To save time on the video. Press Alpha to enter any formulas into these entry lines on my programs. Alpha first. This one is alpha 5 divided by, alway parentheses. You can’t use too many as far as i’m concerned. Parentheses make everything clear. And certainly needed in division or fraction problems. Plus 3 times X minus 4. I always show you what you’ve entered. You can change it if you want. I say it’s okay.We factored the denominator, you noticed there’s two factors here. That means you’re going to be two partial fractions. So, you start by writing five which is the numerator divided by x squared plus 3x minus 4 times the denominator not factored yet. And then you to the partials. A divided by X minus one, which is the first factor and B divided by x plus 4, whic is a second factor. Always set that up. There is no x squares or anything so it’s very simple, here. Now when you multiply both sides by by the denominator you can eliminate a denominator in your left side. So you’re going to get just five and then course, when you do the multiplication in the denominator here,they switch around. A times x plus 4 plus b times x minus one. Now again, we try to we try to look where we can eliminate certain fractions here for factors. So you notice that minus 4 plus four zeros, it would limit this would it would make a minus five here. So anyways, at x equals minus 4. You get 5 is equal to, whenever you do these, you see quotation marks. I can’t put parentheses in the calculator. The way it works so. You’re gonna put parentheses here.Parentheses minus 4, parentheses plus 4. We are inserting this into the function so that you can do the math on it. Parentheses minus 4 parentheses minus 5. You can see B equals minus 5. So B equals minus 1. And same thing here at X equals one. This becomes zero B and this one becomes 5.So A equals one. Partial Fractions are one over x minus or plus -1 over X plus 4. And you do the integrals. You got 1 times log of x minus 1 absolute and minus 1 times log X plus 4 absolute plus C. Integration doesn’t become completed remember integration solves the original funtion, finds the area under the curve of the original function. But when there’s no limit or no range yet, then there’s always a plus C here.Plus constants. If we’ve had a range like from X equals 7 to X equals 10 or something, then we would come up with a number. And that number would be the area under the curve the original function. That’s all integration does, ever. Pretty neat, huh? everystepcalculus.com and everystepphysics.com
Got to my site, think about buying my programs. Thank you.

Filed Under: Partial Fractions

Partial Fraction Example 6

September 16, 2014 by Tommy Leave a Comment

Raw Transcript
Hello Everyone, Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a test problem on Partial Fraction Decomposition, again.Let me show you how my programs work on this. Index 8 to get to my main menu. And we scroll down the Partial Fractions which is in the menu. You can scroll up or down here with the cursor. You have to press Alpha before we enter anything in these entry lines here.Press Alpha and the problem is one divided by, I’m going to use parentheses for the denominator And numerator. This one is x squared minus nine.I always show you what you’ve entered. Now notice that x squared minus nine is a difference of squares so when you factor that it’s always X minus three times x plus three. And that’s a big deal in calculus so always always be on the lookout for these type of things. These difference of squares. Sometimes I’ll have X minus 3 up in the numerator and it will cancel and they use all kinds tricks to throw you off. If you’re hip and I’m gonna try to make you hip, you’re always are looking for the difference in squares. Okay. We’re doing Partial Fractions so I say it’s okay. I’ll always give you a change it if it’s not. And I factor it for you. Here’s x minus three times x plus three. If you can’t factor the denominator, you can’t do Partial Fractions. So keep that in mind, too. And the problems have to be relatively simple in tests because not that many people, including myself, are not very good factoring. In our heads, you know. They get more complicated than this, so. So, you start out by putting one,numerator, divided by x squared minus 9 times x squared minus nine. What you’re doing is multiplying both sides the denominator. This is factored but this is not. And of course, when you multiply the numerator by this, you’re going to eliminate. So there’s going to b one up there. And of course these switch around as we do times this portion here. A divided by x minus three plus B divided by x plus three. I switched it around now so it’s one equals A times x plus three plus b times x minus three. Now the first thing you want to do is eliminate some of these. So you’re going to put a minus three here to make this zero. I’ll do that for you. I have x equals minus three. I put, anytime you see quotation marks, you put parentheses. Parentheses minus three plus three which is zero. B times parentheses minus three parentheses minus three which is minus 6. Zero minus six so one equals a B minus 6. One equals B minus 6 to B is equal to minus one sixth. And X equals three parentheses three in here. open and close plus three And this becomes six and this becomes zero. Which a is equal to one sixth. Partial Fractions, enter one sixth divided by by X minus three plus minus one sixth divided by X plus three. Those are the Partial Fractions. And when you integrate these, one sixth logged absolute value X minus three plus minus one sixth times log absolute value X plus 3. So add all the stuff on your paper and homework, or whatever. Get the problem perfect. Pretty neat, huh? everystepcalculus.com. Go to my site and buy my programs.
Thank you

Filed Under: Partial Fractions

Partial Fraction Decomposition Ex 11

September 7, 2014 by Tommy Leave a Comment

partial-fraction-decomposition-calculus

Filed Under: Partial Fractions

Partial Fractions Example 3

September 6, 2014 by Tommy Leave a Comment

partial-fraction-solver-ex3

Filed Under: Partial Fractions

Partial Fractions of Integral-Video

September 3, 2014 by Tommy Leave a Comment

Raw Transcript
Hello Everyone, Tom for everystepcalculus.com and everystepphysics.com. I’m going to do partial fraction problem. This person said that it’s a hard partial fraction problem. Let’s see about that. It is hard if you ask me, without my programs. But let’s do it. Index 8 to get to my menu. Scroll down to partial fractions. We’re going to enter the integral. You have to press alpha before you enter anything in these entry lines. We’re going to go alpha and then going to do left parentheses, X squared plus 3 times X plus 1 close off the parentheses divided by, open up the parentheses, X to the fourth power plus 5 times X squared plus 4, close off the parentheses.
I always show you what you’ve entered. Now maybe you’re better than I am but you have to factor this denominator in partial fractions every time. So this it makes it hard for a class in it for a test problem is way too hard for a test probably for homework because I don’t know who would be able to write off from memory to factor that. I say it’s okay. We factor the denominator; here it is right here. And we start doing our partials. The idea is that you are going to deliminate the denominator here by multiplying at times the same thing with the numerator this. This here is the the factored part ion is here and this is the original denominator. And so then we have
the numerator is equal to Ax plus B times x square plus 4 plus Cx plus D times x squared plus 1.You multiply that out using the foil method. Remember the foil method? First outside inside and last. First would be Ax times x squared,outside would be Ax times four, et cetera. I multiply it out here. The calculator uses small letters rather than capitals. No problem. They combine those terms and come up with this. A plus C is x squared, x squared, 4a plus c, et cetera. Now we have to figure out the coefficients for this numerator. And since there’s no X cubed, we have to put one in there, which is 0 times x cubed. And then we have one coefficient here, three coefficient here, and one. So here we have one, three, and one. So then therefore AC is equal to 0, BD equal to one. 4a plus c is equal to three and 4b plus d is equal to one. And we work out, we use subtraction. We’re subtracting like terms. So AC is subtracted. 4a plus c and that equals three. A equals one. Do the same for each one of them. D equals one, C equals a minus one. Notice here we’re replacing A with what we found which is one. Which I do that for you here. When they’re in quotation marks, I replaced it in there. Partial fractions are this. Right here. And I also do the integrals for you. Log of x squared plus one divided by two, et cetera, et cetera. Pretty neat, huh?
everystepcalculus.com. Go to my site and buy my programs.
Thank you

Filed Under: Partial Fractions

Partial Fractions

August 26, 2014 by Tommy Leave a Comment

Let’s talk about partial fractions and what I’ve found out after programming them. Partial fractions would never occur in real life. Remember the integral is the area under a smooth curve, nothing more from my knowledge, when you graph any original function; it has at least 2 asymptotes. Well that eliminates the smooth curve. Remember an asymptote is a vertical line or sometimes horizontal line where the original function never touches to infinity, so if you choose a range that goes (crosses) over that asymptote there is no computed answer, so no area under a smooth curve. So partial fractions are a Sudoku of math problem, like so many of calculus problems. So let’s get into what I’ve found in programming this area of calculus. The denominator has to be factored to produce partial fractions. Sometimes there are two factors, then three, then two factors with an exponent in between the parenthesis, then even one factor with an exponent outside the parenthesis. The factored denominator is the key as to how to approach the problem.

In my programs, I have a whole separate program to decide if there are two factors or three or any other choices. Most of us are not good at factoring. Maybe simple functions we can, like the difference of squares (x^2-9) = (x-3)(x+3). When it gets a little deeper that this most of us are lost. For instance, what’s the factors of (x^3-x) or (x^4+7x^3+6x^2)? The calculator knows and because of that, so does my programs. But would those appear in your test? In my opinion if they did then most of the class would fail that. No question about it. Let alone complete the partial fractions. So enough about factoring. Remember in algebra when they said you could do anything to one side of an equation as long as you do it to the other side also. They do this in partial fractions. On the left side of the equation in partial fractions they multiply the original function by the denominator, which effectively gets rid of the denominator. Well they do the same thing on the other side (except factored) to get rid of the added or subtracted fractions, and change the A / (x-1) to a product through common denominator. That said, a few trick to remember in partial fractions. If in the factored denominator you have (x^2+6) for the first factor so you want to set that up for partial fractions you would go Ax+B / (x^2+6), if the second factor was (x^2-3) you’d set this up as (Cx+D) / (x^2-3), Do you understand this? Very important and no exceptions!! If the factor turned out to be (x-5)^5(exponent outside of the parenthesis), this is called re-occurring powers, or exponents, and the factors are A/(x-5)^1 + B/(x-5)^2+C/(x-5)^3+E/(x-5)^4+F/(x-5)^5. Now if the power in the denominator is less or equal to the power in the numerator, you have to use short division to find the remainder to the partials.

My programs do all of this for you, as I required my programming to do for me also when I was in class. Hey good luck in your class, I’m always available to help you if you just ask.

Filed Under: Partial Fractions

Partial Fractions Example 10-Video

August 24, 2014 by Tommy Leave a Comment

Partial 9

Filed Under: Partial Fractions

Partial Fractions | Example 9-Video

August 24, 2014 by Tommy Leave a Comment

partial-fractions-calculus

Raw Transcript

Hello Everyone, Tom from everystepcalculus.com and everystepphysics.com. Partial Fraction Decomposition. This time with three Partial Fractions.Let’s get started.Put index 8 in here with the open and closed parentheses, you get to my menu.You can scroll down to start up in the a section but you can scroll down alphabetical to Partial Fractions.Enter the integral by pressing Alpha first. Alpha, parentheses X squared plus 12 times X plus 12,close off the parentheses, divided by, open parentheses X cubed minus 4 times X. I always show you what you’ve entered. How many of you could factor this here? It’s pretty tough, I would think. Do it easy on my program. It comes up with 3 factors. So you write this in your paper. X squared plus 12x plus 12 is the numerator. Divided by the denominator times the denominator. And this is the actual denominator factored so we do the same thing here. And we’re going to use this to multiply times all of this to get rid of all the divisions. Common denominator is the actual words. So we added with x squared plus 12x plus 12 equals A and x times x minus 2 times x plus 2 Bx times x plus 2 Cx times x minus 2 And x equals 2. These quotation marks here is what the calculator does but you would put parentheses wherever you see these. parentheses 2 squared. You’re substituting 2 for every x in these functions. Use parentheses 2 here plus 12, etc. Do that throughout the whole system here. And that turns out to be B equals 5. At x equals zero. Use 0 for every x in all the computations here. And that turns out to be A equals minus 3 and x equals minus 2. Substitute for x in all the equation. C equals minus 1. Partial Fractions are minus 3 over x plus 5 over x minus two plus minus one over x plus two. And we integrate those. One thing about integrating a denominator with no, no exponent. You notice you can’t. This is an exponent of one, theoretically. But if you try to switch it to the numerator, five times X minus 2, it becomes a minus 1. Well in integration, you’re going to add one and then divide by the result. Well if you add one to a minus one, you get zero. In the numerator, anything to the zero is one. So that’s the reason you have to use logs. Whenever you see a no exponent to the denominator, it’s a log integration. So minus three logged minus the absolute X 5 log absolute x minus two minus one log x plus 2 plus C. Pretty neat, huh? everystepcalculus.com
Go to my site and buy my programs.
Thank you for watching.

Filed Under: Partial Fractions

Partial Fraction Decomposition on TI-89

March 30, 2014 by Tommy Leave a Comment

Partial Fraction Decomposition on TI-89

Raw Transcript

This is a video from EveryStepCalculus.com demonstrating how my programs work on a TI-89 Titanium calculator and other calculators in the TI system for physics and calculus problems.

Okay, Partial Fraction Decomposition. Let’s get started, to get to my menu you have to press 2nd alpha to put the i_n_d_e_x in here you have to press alpha to put the 9 (). Press Enter and you’re into my menu. Scroll down to wherever you want all the way up and down.

But I’m at Partial Fractions right now which we want to do and we’re going to enter our function. You always have to Press alpha before you enter anything in a these entry lines in my programs. So Alpha we’re gonna do a quantity of 4 times X plus 9, divided by the quantity X minus 1, times the quantity of x plus 1, times the quantity of X plus 4.

I always show you what you’ve entered so you can change in case you made a mistake and we’re into the problem. You factored the denominator. It’s already factored here but in case it wasn’t, I would. And then you multiply, you multiply by the factor of the denominator. You get these. They’re all exactly right. Mark it down on your paper exactly like you see it. And if x = 1, the idea is that you cancel certain factors, certain variables. And here’s when you put -1 the function here is where they all set.

Mark that on your paper, turns out to be 5=A*(0)+B*(-6)+C*(0) 5=B*(-6) 5/-6. Mark all that on your paper. X equals one which will negate the second term. You mark these all these… put all these in replace or um x in your function there. A couple of them become zeros so that you can solve so a equals 13 tenths. And then you have enough variables, enough answers to solve the other c. Here’s the answer.

Pretty neat, huh? EveryStepCalculus.com. Go to my site, buy my programs and pass calculus.

More Partial Fraction test questions solved on your TI-89 calculator

Partial Fraction Test Question #1

Partial Fraction Test Question #2

Partial Fraction Test Question #3

Filed Under: Partial Fractions

Partial Fraction Decomposition Video

March 16, 2014 by Tommy Leave a Comment

Partial Fraction Decomposition on the TI-89

Raw Transcript

Hello everyone, Tom from everystepcalculus.com, going to do a partial fraction decomposition right now, letís get started.
Index 7 if you bought both programs and loaded them into the calculator with the instructions and youíre going to scroll to partial fractions, thatís what we want to do with the problem and weíre going to add our function, you have to press alpha before you add anything in this entry lines here. Alpha four divided by parenthesis parenthesis three times X minus one close up parenthesis times X and it will show you what youíve entered and notice this is already factored, this is actually three X squared minus X but itís already been factored here in this problem and we say itís ok, it allows you to change it in case you made a mistake, so here is the factoring of it, you always the denominator, if the denominator canít be factored itís not a partial fraction *** your problem, then we go through the calculations. A is over X and B is over 3X-1 and we multiply times the factoring because we want to eliminate this from the other side, when we multiply something thatís been divided we can eliminate it and it also makes these into linear variables such as this and then we try to make one zero so we could solve for the other one which we do here and B equals 12, Iíll go through it quick, now we have X equal to zero and so A equals -4 and hereís the answer, the partial fraction here is -4/X + 12 and when you do the X integration of it, it becomes a log problem and I do that for you too, -4 log of log of absolute value of X + 12 log of 3X, pretty neat, everystepcalculus.com, go to my site, buy my programs, pass your calculus class and also subscribe to new videos if you want at my channel.

Filed Under: Partial Fractions Tagged With: partial fraction decomposition

Partial Fractions 4 on the Ti89 | Every Step Calculus Video

October 15, 2013 by Tommy Leave a Comment

Partial Fractions Decomposition 4 on TI-89

Raw Transcript

This is a video from EveryStepCalculus.com demonstrating how my programs work on a TI 89 Titanium calculator and other calculators in a TI system for physics and calculus problems.

Okay, partial fraction decomposition. All my programs work on, many people have asked for that so I programmed it. Um, to get to my menu you have two press second Alpha to put I_N_D_E_X. This is a calculus two and three Series and then you have to press Alpha again to put the 9 in the open and close parentheses and press Enter and then your into my menu.

I’m already at partial fractions here all are alphabetical you scroll down to it. Choose that, press Enter, give an example with what it should look like. When you enter it you have to press Alpha before you enter anything in these empty lines here.

Going to go Alpha for quantity, you have to use parenthesis now. We’re doing quantities in numerators and quantities in denominators. So the quantity X squared plus 8 divided by quantity X squared minus 5 times X plus six now you want to do this without from memory without my programs be my guest.

I always show you what you’ve entered, so you can change in case you made a mistake I say it’s okay and the first thing you do is factor the denominator which is this. You write this on your paper exactly as you see it and so the numerator is equal to these but put the a and b partial fractions in. You multiply it times the common denominator. Actually this is on the other side to x squared plus eight over this amount but when you multiply it out it cancels and x squared plus 8 equals a times X minus 2 plus b X minus 3.

You choose a number that will cancel the one of them, so you can solve it and you choose 2 so you got your, these in quotation marks are entered for the x’s x squared plus 8 here’s 2 minus 2 etcetera. You write that on your paper. I show you what the answer is and you work it out and you come up with b minus 12. And you write down on your paper, that x equals three.

Mark that into the equation and it equals this and then you work out the computations in a equals 17 so the partial fractions 17 over x-3 plus -12 or x-2.

Pretty neat huh, EveryStepCalculus.com go to my site by my programs and pass calculus.

Filed Under: Partial Fractions Tagged With: partial fraction decomposition, Partial Fractions 4

Partial Fractions Decomposition Video

August 29, 2013 by Tommy Leave a Comment

Raw Transcript

This is a video from EveryStepCalculus.com demonstrating how my programs work on a TI-89 Titanium calculator and other calculators in the TI system for physics and calculus problems
okay partial fractions. Uh, to get started on my programs you have to press 2nd Alpha to put in i_n_d_e_x in here then press. Alpha to put the 9 in open and close parentheses press enter and your into my menu. I’m already at partial fractions you see there’s a menu here, all alphabetical that
you can scroll down to up to we want partial fractions right now you have to press Alpha before you put in anything into these entry lines here remember to press Alpha and put in the function 1 divided by the quantity x squared plus 2 times x, I’ve already showed you what you’ve entered so you can change it if you want. I say it’s okay first of all we factor the denominator it’s already factored here and we choose our A&B and b would be x and x plus 2, equals 1 and then we multiply by the common denominator which I showed you in the previews one you get x, or a times x plus 2 plus b times x trying to eliminate one parameters one variable a in this case so we multiply by a -2 or I mean add by a -2 we’ll get a zero so we choose that one and then we figure out what b is, and then we can use that to figure out what a is and here’s a and your three halves, here’s your partial thing for your answer for your calculus test pretty neat huh? EveryStepCalculus.com goto my site buy my programs and pass calculus.

Filed Under: Partial Fractions Tagged With: Partial Fractions 3B

BUY NOW and get 500+ Calculus Programs Inside your TI-89 Series Calculator

Buy Now

Recent Testimonials 2022

You are an angel sent from above TOM!!! Thank you so much for being patient with me. I got the programs to work and I am very confident I am going to pass this class once and for all. The Double and Triple Integrals programs are a life saver! Thank You Thank You Thank You!

-Cotto

Tom-    I showed my ex, who is a calculus professor, and he was waaaaaaay impressed. And he is an arrogant ass, who never helped me ever...I could tell he wanted to hate on it, but he couldnt. 

Kristin P

Tom...I think that I’m finally done with Calculus II. In the prior test I got 78 and yesterday I finished all the problem on the test. I think I should be able to remain around the same grade. Thank you so much for your help; your programs really made the difference. They didn’t just solve the problems for you, in my case, they gave me the confidence and security I had lost with those stupid professors and the way they teach. To be honest, studying the programs on my calculator taught  me how to solve problems that I couldn’t do before due to the way they were presented. I felt confident and secure yesterday, and it only possible because either I remember  how to do the problems or the calculator would. Thanks one more time for time, dedication and quick responses. There is no other person in the whole world that would do what you do for us , college students being  killed  with freaking calculus classes.      John

Tom-     Got it to work with that link you sent me!  Just wanted to say thanks for all the great work you do, and for helping me pass this calculus class.  I'm going to tell everyone about this and make them pay the $30 dollars because you have done a splendid job programming my friend.  Let me know if you have any new programs for derivatives or integrals and Ill let you know if I need any more help!  Much thanks,                -Eric

I basically just needed to say that you're an amazing man. Basically saved my life during my emag theory course    

-DoubtingThomas  (Youtube vectors review here)

oh my god I figured it out. You're the freaking best!      -Sarah

Thanks Tom. I appreciate you taking the time to break down and explain these to me. :0)     -Nelson

 Tommy,     Great talking with you last night. I already liked you for developing this “most excellent program” but after our conversation I concluded you to be a great guy. I’ve been playing with this program most of the night, took in a few “z’s” and am back for more. This program really is superb. I did, however, notice that for some unknown reason when I attempt to do Relative Extrema’s and Trajectories that both programs came up as “Program not Found”. I’m not sure if I will be encountering the Trajectory stuff in this semester of Calculus but I do have a test this Thursday that includes Relative Extrema. Any suggestion, oh Master of this great creation?! I’m going to be gone most the day but should be home late afternoon if you got time to call. Same number (843-xxx-xxxx). That’s Myrtle Beach, 3 hours ahead of you and more golf courses than you can shake a stick at. Thanks    -Joe

Wow! Awesome! These are great, so great, thank you!            -Kristen

Tom is the man! His program is helping me pass my calculus class. He was willing to help me immediately when I couldn't get one of the programs working! This application is in my opinion a STEAL! I've never met Tom in person but I'll owe passing this class to every step calculus.

Copyright © 2025 · Genesis Sample Theme on Genesis Framework · WordPress · Log in