In Exercises 1–8, write the form of the partial fraction decompos...

Question

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.(11x - 10)/(x − 2) (x + 1)

Accepted Answer

Welcome back. I am so glad you're here. We are given the expression 28 X minus divided by x minus nine times X plus five. And we are asked to rewrite this in its partial fraction decomposition form but we do not have to solve for the constants. Yay, all right. We recall from previous lessons on partial fraction decomposition that we're going to look at the denominator. The denominator is already factored for us. Great. So now we're going to ask ourselves two questions about those factors in the denominator. The first question is, are these linear or quadratic factors an x minus nine that X has a degree of one that is linear and X plus five. That also has a degree of one. So that is also a linear factor. Great. The next question we're going to ask ourselves about these factors is if they are distinct or repeated in x minus nine. There's only one of those and x plus five. There's only one of those. These are both distinct. Great, We've answered those two questions. So now we set this equal to and we ask ourselves, how many factors were there? There are two x minus nine and X plus five. So we're going to have to new fractions added together. We'll work on the denominators first. The denominator for our first new fraction is going to be that first factor X -9. And the denominator for our second fraction is going to be that second factor X plus five. And now we'll work on the numerator because x minus nine and x plus five are both linear. The numerator is for both of those two fractions are going to be constant terms, so the numerator for x minus nine is going to be A and the numerator for X plus five is going to be B. And because we don't have to solve for the constants, we are done. We look at our answer choices and this matches with answer choice. A. Well done. We'll catch you on the next one.

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.(11x - 10)/(x − 2) (x + 1)

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