Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set: 38

Answer

$\dfrac{x^{2}-y^{2}}{3x^{2}+3xy}\cdot\dfrac{3x^{2}+6x}{3x^{2}-2xy-y^{2}}=\dfrac{x+2}{3x+y}$

Work Step by Step

$\dfrac{x^{2}-y^{2}}{3x^{2}+3xy}\cdot\dfrac{3x^{2}+6x}{3x^{2}-2xy-y^{2}}$ Factor both rational expressions completely: $\dfrac{x^{2}-y^{2}}{3x^{2}+3xy}\cdot\dfrac{3x^{2}+6x}{3x^{2}-2xy-y^{2}}=\dfrac{(x-y)(x+y)}{3x(x+y)}\cdot\dfrac{3x(x+2)}{(x-y)(3x+y)}$ Evaluate the product of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{3x(x-y)(x+y)(x+2)}{3x(x+y)(x-y)(3x+y)}=\dfrac{x+2}{3x+y}$
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