Intermediate Algebra (6th Edition)

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

Chapter 6 - Review - Page 405: 95

Answer

$\dfrac{2}{15-2x}$

Work Step by Step

The given expression, $ \dfrac{\dfrac{1}{x}-\dfrac{2}{3x}}{\dfrac{5}{2x}-\dfrac{1}{3}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{3(1)-1(2)}{3x}}{\dfrac{3(5)-2x(1)}{6x}} \\\\= \dfrac{\dfrac{3-2}{3x}}{\dfrac{15-2x}{6x}} \\\\= \dfrac{\dfrac{1}{3x}}{\dfrac{15-2x}{6x}} \\\\= \dfrac{1}{3x}\div\dfrac{15-2x}{6x} \\\\= \dfrac{1}{3x}\cdot\dfrac{6x}{15-2x} \\\\= \dfrac{1}{\cancel{3x}}\cdot\dfrac{\cancel{3x}\cdot2}{15-2x} \\\\= \dfrac{2}{15-2x} .\end{array}
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