Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises: 90

Answer

$\dfrac{2(x-y)}{\sqrt{x}-\sqrt{y}}=2\sqrt{x}+2\sqrt{y}$

Work Step by Step

$\dfrac{2(x-y)}{\sqrt{x}-\sqrt{y}}$ Multiply both numerator and denominator by $\sqrt{x}+\sqrt{y}$ and simplify: $\dfrac{2(x-y)}{\sqrt{x}-\sqrt{y}}=\Big(\dfrac{2(x-y)}{\sqrt{x}-\sqrt{y}}\Big)\Big(\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{x}+\sqrt{y}}\Big)=...$ $...=\dfrac{2(x-y)(\sqrt{x}+\sqrt{y})}{x-y}=2\sqrt{x}+2\sqrt{y}$
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