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 - Page 445: 52

Answer

$\dfrac{4\sqrt{ax}+2\sqrt{ay}}{4x-y}$

Work Step by Step

Rationalizing the denominator of $ \dfrac{2\sqrt{a}}{2\sqrt{x}-\sqrt{y}} $ results to \begin{array}{l} \dfrac{2\sqrt{a}}{2\sqrt{x}-\sqrt{y}} \cdot \dfrac{2\sqrt{x}+\sqrt{y}}{2\sqrt{x}+\sqrt{y}} \\\\= \dfrac{4\sqrt{ax}+2\sqrt{ay}}{(2\sqrt{x})^2-(\sqrt{y})^2} \\\\= \dfrac{4\sqrt{ax}+2\sqrt{ay}}{4x-y} .\end{array}
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