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: 71



Work Step by Step

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