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: 67


$\displaystyle \frac{4(x+y)}{3(x-y)}$

Work Step by Step

Factor what we can: $x^{2}+2xy+y^{2}$ = (square of a sum) = $(x+y)^{2}$ $x^{2}-2xy+y^{2}$ = (square of a difference) = $(x-y)^{2}$ $4x-4y$ = $4(x-y)$ $3x+3y=3(x+y)$ Rewrite the problem: $\displaystyle \frac{(x+y)(x+y)}{(x-y)(x-y)}\cdot\frac{4(x-y)}{3(x+y)}=\qquad$ ... reduce common factors =$\displaystyle \frac{(1)(x+y)}{(1)(x-y)}\cdot\frac{4(1)}{3(1)}=$ =$\displaystyle \frac{4(x+y)}{3(x-y)}$
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