Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set: 66

Answer

$\dfrac{\sqrt{xz}+z}{x-z}$

Work Step by Step

Multiplying by the conjugate of the denominator, the rationalized-denominator form of the given expression, $ \dfrac{\sqrt{z}}{\sqrt{x}-\sqrt{z}} ,$ is \begin{array}{l}\require{cancel} \dfrac{\sqrt{z}}{\sqrt{x}-\sqrt{z}}\cdot\dfrac{\sqrt{x}+\sqrt{z}}{\sqrt{x}+\sqrt{z}} \\\\= \dfrac{\sqrt{z}(\sqrt{x})+\sqrt{z}(\sqrt{z})}{(\sqrt{x})^2-(\sqrt{z})^2} \\\\= \dfrac{\sqrt{z(x)}+\sqrt{z(z)}}{x-z} \\\\= \dfrac{\sqrt{xz}+\sqrt{(z)^2}}{x-z} \\\\= \dfrac{\sqrt{xz}+z}{x-z} .\end{array}
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