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: 74

Answer

$\dfrac{2(2x-3)}{3(6+x)}$

Work Step by Step

The given expression, $ \left( \dfrac{2}{3}-\dfrac{1}{x} \right)\div\left( \dfrac{3}{x}+\dfrac{1}{2} \right) ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{x(2)-3(1)}{3x}\div\dfrac{2(3)+x(1)}{2x} \\\\ \dfrac{2x-3}{3x}\div\dfrac{6+x}{2x} \\\\ \dfrac{2x-3}{3x}\cdot\dfrac{2x}{6+x} \\\\ \dfrac{2x-3}{3\cancel{x}}\cdot\dfrac{2\cancel{x}}{6+x} \\\\ \dfrac{2(2x-3)}{3(6+x)} .\end{array}
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