Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 551: 103

Answer

$\frac{1}{(x+y)(\sqrt x- \sqrt y)}$.

Work Step by Step

The given expression is $=\frac{\sqrt x+ \sqrt y}{x^2-y^2}$ Use the special formula $A^2-B^2=(A+B)(A-B)$. $=\frac{\sqrt x+ \sqrt y}{(x+y)(x-y)}$ The conjugate of the numerator is $\sqrt x- \sqrt y$. Multiply the numerator and the denominator by $\sqrt x- \sqrt y$. $=\frac{\sqrt x+ \sqrt y}{(x+y)(x-y)}\cdot \frac{\sqrt x- \sqrt y}{\sqrt x- \sqrt y}$ Use the special formula $(A+B)(A-B)=A^2-B^2$. $=\frac{(\sqrt x)^2- (\sqrt y)^2}{(x+y)(x-y)(\sqrt x- \sqrt y)}$ Simplify. $=\frac{x -y}{(x+y)(x-y)(\sqrt x- \sqrt y)}$ Cancel common terms. $=\frac{1}{(x+y)(\sqrt x- \sqrt y)}$.
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