Intermediate Algebra (6th Edition)

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

Chapter 6 - Review - Page 405: 98

Answer

$\dfrac{5x}{2}$

Work Step by Step

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