Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set: 41

Answer

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

Work Step by Step

$\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}}$ Multiply the numerator and the denominator of this expression by the conjugate of the denominator and simplify if possible: $\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}}=\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}}\cdot\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}=\dfrac{\sqrt{x}(\sqrt{x}-\sqrt{y})}{(\sqrt{x})^{2}-(\sqrt{y})^{2}}=...$ $...=\dfrac{\sqrt{x^{2}}-\sqrt{xy}}{x-y}=\dfrac{x-\sqrt{xy}}{x-y}$
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