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: 38

Answer

$\frac{y+3}{y-3}$.

Work Step by Step

The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$. The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$. Hence here: $\frac{y^2-9}{y^2-6y+9}=\frac{y^2-3^2}{y^2-2\cdot y\cdot3+3^2}=\frac{(y+3)(y-3)}{(y-3)^2}=\frac{y+3}{y-3}$.
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