Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set: 82



Work Step by Step

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