Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - 7.3 - Adding and Subtracting Algebraic Fractions - Problem Set 7.3: 77

Answer

$\frac{-6x+21}{(x-2)(x+1)}$

Work Step by Step

By inspection, we see that the LCM of the denominators is $(x-2)(x+1)$. Therefore, we create a common denominator using this LCM and obtain: $\frac{3}{x-2}-\frac{9}{x+1}$ =$\frac{3(x+1)-9(x-2)}{(x-2)(x+1)}$ =$\frac{3x+3-9x+18}{(x-2)(x+1)}$ =$\frac{-6x+21}{(x-2)(x+1)}$
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