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: 33


$\frac{4}{y+5}$ (and $y\ne5$).

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: $\frac{4y-20}{y^2-25}=\frac{4(y-5)}{y^2-5^2}=\frac{4(y-5)}{(y+5)(y-5)}=\frac{4}{y+5}$ (and $y\ne5$).
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