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: 73

Answer

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

Work Step by Step

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