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. (7x^2 -9x+3)/(x²+7)²

Accepted Answer

Welcome back, I am so glad you're here. We are given this expression three X squared minus X plus 25 divided by x squared plus 11 squared. And we are asked to rewrite this in its partial fraction decomposition form. But we don't have to solve for the constance. Alright. We recall from previous lessons on partial fraction decomposition that we are going to look at the denominator. And the first thing we're going to ask ourselves is are the factors in our denominator linear or quadratic. And we've got X squared plus 11, that has a degree of two for that act So we are dealing with quadratic factors here. And the next step is to ask ourselves if the factors and our denominator are distinct or repeated and X squared plus 11 is squared. So that is a repeating factor. And so when we have a quadratic factors that are repeated, we are going to set our original expression equal to and we can set up our denominators first. So because we have two factors there, we're going to have two fractions. And because they're repeating the first denominator is going to be our original X squared plus 11 factor but it won't be squared. So that's our original quadratic factor but not repeated. And for the second one we'll have it just as is X squared plus 11 squared. So those are our denominators. And now because these are quadratic factors in the denominator, our numerator are going to be linear. So for the first fraction, that's going to be the linear A X plus B. And for the second one, that's going to be the linear C. X plus D. And now, because we don't have to solve for the constant terms for A. B, C and D, we're done, we take a 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. (7x^2 -9x+3)/(x²+7)²

Key Concepts

Rational Expressions

Partial Fraction Decomposition

Polynomial Degree and Factorization

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