College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.7 - Rational Expressions - R.7 Assess Your Understanding - Page 71: 48


$\dfrac{-3x-35}{(x+5)(x-5)}; x \ne -5, 5$

Work Step by Step

The LCM of $x+5$ and $x-5$ is $(x+5)(x-5)$. Use the LCM as the expressions' LCD to make them similar: $=\dfrac{2\color{blue}{(x-5)}}{(x+5)\color{blue}{(x-5)}} -\dfrac{5\color{blue}{(x+5)}}{(x-5)\color{blue}{(x+5)}} \\=\dfrac{2x-10}{(x+5)(x-5)}-\dfrac{5x+25}{(x-5)(x+5)}$ The expressions are similar so subtract the numerators and copy the denominator to obtain: $=\dfrac{2x-10-(5x+25)}{(x+5)(x-5)} \\=\dfrac{2x-10-5x-25}{(x+5)(x-5)} \\=\dfrac{-3x-35}{(x+5)(x-5)}; x \ne -5, 5$
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