Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set: 81

Answer

$-\dfrac{32}{x(x+2)(x-2)}$

Work Step by Step

The given expression, $ \dfrac{4}{x}\cdot\left( \dfrac{2}{x+2}-\dfrac{2}{x-2} \right) ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{4}{x}\cdot\dfrac{(x-2)(2)-(x+2)(2)}{(x+2)(x-2)} \\\\= \dfrac{4}{x}\cdot\dfrac{2x-4-(2x+4)}{(x+2)(x-2)} \\\\= \dfrac{4}{x}\cdot\dfrac{2x-4-2x-4}{(x+2)(x-2)} \\\\= \dfrac{4}{x}\cdot\dfrac{-8}{(x+2)(x-2)} \\\\= \dfrac{-32}{x(x+2)(x-2)} \\\\= -\dfrac{32}{x(x+2)(x-2)} .\end{array}
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