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: 75

Answer

$\dfrac{4a^2}{9(a-1)}$

Work Step by Step

The given expression, $ \left( \dfrac{2a}{3} \right)^2\div\left( \dfrac{a^2}{a+1}-\dfrac{1}{a+1} \right) ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{4a^2}{9}\div\dfrac{a^2-1}{a+1} \\\\ \dfrac{4a^2}{9}\div\dfrac{(a+1)(a-1)}{a+1} \\\\ \dfrac{4a^2}{9}\cdot\dfrac{a+1}{(a+1)(a-1)} \\\\ \dfrac{4a^2}{9}\cdot\dfrac{\cancel{a+1}}{(\cancel{a+1})(a-1)} \\\\ \dfrac{4a^2}{9(a-1)} .\end{array}
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