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: 51

Answer

$\dfrac{x-\sqrt{xy}}{x-y}$

Work Step by Step

Rationalizing the denominator of $ \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}} $ results to \begin{array}{l} \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}} \cdot \dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}} \\\\= \dfrac{x-\sqrt{xy}}{(\sqrt{x})^2-(\sqrt{y})^2} \\\\= \dfrac{x-\sqrt{xy}}{x-y} .\end{array}
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