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: 72

Answer

$\dfrac{3}{x}$

Work Step by Step

The given expression, $ \left( \dfrac{1}{2}+\dfrac{2}{x} \right) - \left( \dfrac{1}{2}-\dfrac{1}{x} \right) ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{x(1)+2(2)}{2x} - \dfrac{x(1)-2(1)}{2x} \\\\ \dfrac{x+4}{2x} - \dfrac{x-2}{2x} \\\\ \dfrac{x+4-(x-2)}{2x} \\\\ \dfrac{x+4-x+2}{2x} \\\\ \dfrac{6}{2x} \\\\ \dfrac{\cancel{2}\cdot3}{\cancel{2}x} \\\\ \dfrac{3}{x} .\end{array}
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