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: 75

Answer

$\Big(\dfrac{x^{2}-y^{2}}{x^{2}+y^{2}}\div\dfrac{x^{2}-y^{2}}{3x}\Big)\cdot\dfrac{x^{2}+y^{2}}{6}=\dfrac{x}{2}$

Work Step by Step

$\Big(\dfrac{x^{2}-y^{2}}{x^{2}+y^{2}}\div\dfrac{x^{2}-y^{2}}{3x}\Big)\cdot\dfrac{x^{2}+y^{2}}{6}$ Factor the numerators of the two rational expressions inside the parentheses: $\Big(\dfrac{(x+y)(x-y)}{x^{2}+y^{2}}\div\dfrac{(x-y)(x+y)}{3x}\Big)\cdot\dfrac{x^{2}+y^{2}}{6}=...$ Evaluate the division of the two rational expressions inside the parentheses: $...=\dfrac{3x(x+y)(x-y)}{(x^{2}+y^{2})(x-y)(x+y)}\cdot\dfrac{x^{2}+y^{2}}{6}=...$ Now, evaluate the product and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{3x(x^{2}+y^{2})(x+y)(x-y)}{6(x^{2}+y^{2})(x-y)(x+y)}=\dfrac{3x}{6}=\dfrac{x}{2}$
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