### 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.