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 - Page 355: 76



Work Step by Step

The given expression, $ \left( \dfrac{x+2}{2x}-\dfrac{x-2}{2x} \right)\cdot\left( \dfrac{5x}{4} \right)^2 ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{x+2-(x-2)}{2x}\cdot\dfrac{25x^2}{16} \\\\= \dfrac{x+2-x+2}{2x}\cdot\dfrac{25x^2}{16} \\\\= \dfrac{4}{2x}\cdot\dfrac{25x^2}{16} \\\\= \dfrac{\cancel{4}}{2\cancel{x}}\cdot\dfrac{25\cancel{x}\cdot x}{\cancel{4}\cdot4} \\\\= \dfrac{25x}{8} .\end{array}
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