Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.5 Rational Expressions - R.5 Exercises: 61

Answer

$\color{blue}{\dfrac{2x}{(x-z)(x+z)}}$

Work Step by Step

The expressions are not similar since they have different denominators. Make the expressions similar using their LCD $(x+z)(x-z)$ to obtain: $=\dfrac{1\color{red}{(x-z)}}{(x+z)\color{red}{(x-z)}} + \dfrac{1\color{red}{(x+z)}}{(x-z)\color{red}{(x+z)}} \\=\dfrac{x-z}{(x+z)(x-z)}+\dfrac{x+z}{(x-z)(x+z)}$ Add the numerators and copy the denominators to obtain: $=\dfrac{(x-z)+(x+z)}{(x-z)(x+z)} \\=\dfrac{(x+x)+(z-z)}{(x-z)(x+z)} \\=\color{blue}{\dfrac{2x}{(x-z)(x+z)}}$
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