College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 90

Answer

$2\sqrt{x}+2\sqrt{y}$

Work Step by Step

We simplify the fraction by multiplying through by $\sqrt{x}+\sqrt{y}$ and using the fact that $(a-b)(a+b)=a^2-b^2$: $\displaystyle \frac{2(x-y)}{\sqrt{x}-\sqrt{y}}=\frac{2(x-y)}{\sqrt{x}-\sqrt{y}} \displaystyle \frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}+\sqrt{y}}=\frac{2(x-y)(\sqrt{x}+\sqrt{y})}{x-y}=2(\sqrt{x}+\sqrt{y})=2\sqrt{x}+2\sqrt{y}$
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