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 - Page 661: 65



Work Step by Step

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