Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.1 - Rational Expressions and Functions; Multiplying and Dividing - Exercise Set - Page 414: 36


$\frac{-1}{5x+2}$ (and $x\ne\frac{5}{2}$).

Work Step by Step

The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$. Hence here: $\frac{5x-2}{4-25x^2}=\frac{5x-2}{-((5x)^2-2^2)}=\frac{5x-2}{-(5x+2)(5x-2)}=\frac{-1}{5x+2}$ (and $x\ne\frac{5}{2}$).
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