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: 42

Answer

$\dfrac{2\sqrt{a}}{2\sqrt{x}-\sqrt{y}}=\dfrac{2(2\sqrt{ax}+\sqrt{ay})}{4x-y}$

Work Step by Step

$\dfrac{2\sqrt{a}}{2\sqrt{x}-\sqrt{y}}$ Multiply the numerator and the denominator of this expression by the conjugate of the denominator and simplify if possible: $\dfrac{2\sqrt{a}}{2\sqrt{x}-\sqrt{y}}=\dfrac{2\sqrt{a}}{2\sqrt{x}-\sqrt{y}}\cdot\dfrac{2\sqrt{x}+\sqrt{y}}{2\sqrt{x}+\sqrt{y}}=...$ $...=\dfrac{(2\sqrt{a})(2\sqrt{x}+\sqrt{y})}{(2\sqrt{x})^{2}-(\sqrt{y})^{2}}=\dfrac{4\sqrt{ax}+2\sqrt{ay}}{4x-y}=...$ We can take out common factor $2$ from the numerator to provide a more simplified answer: $...=\dfrac{2(2\sqrt{ax}+\sqrt{ay})}{4x-y}$
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