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: 34


$\frac{6}{y+7}$ (and $y\ne7$).

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: $\frac{6y-42}{y^2-49}=\frac{6(y-7)}{y^2-7^2}=\frac{6(y-7)}{(y+7)(y-7)}=\frac{6}{y+7}$ (and $y\ne7$).
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