Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.2 - Systems of Linear Equations in Three Variables - Exercise Set - Page 832: 59


The simplified form of the expression $\frac{3}{x-4}-\frac{2}{x+2}$ is $\frac{x+14}{{{x}^{2}}-6x+8}$.

Work Step by Step

Let us consider the expression $\frac{3}{x-4}-\frac{2}{x+2}$ And simplify: $\begin{align} & \frac{3}{x-4}-\frac{2}{x+2}=\frac{3\left( x+2 \right)-2\left( x-4 \right)}{\left( x-2 \right)\left( x-4 \right)} \\ & =\frac{3x+6-2x+8}{{{x}^{2}}-6x+8} \\ & =\frac{x+14}{{{x}^{2}}-6x+8} \end{align}$ Therefore, $\frac{3}{x-4}-\frac{2}{x+2}=\frac{x+14}{{{x}^{2}}-6x+8}$ Thus, the simplified form of the expression $\frac{3}{x-4}-\frac{2}{x+2}$ is $\frac{x+14}{{{x}^{2}}-6x+8}$.
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