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 550: 81


$\displaystyle \frac{a+\sqrt{ab}}{a-b}$

Work Step by Step

We lose the square roots in the denominator by applying the difference of squares formula: $(a\sqrt{x}+b\sqrt{y})(a\sqrt{x}-b\sqrt{y})=(a\sqrt{x})^{2}-(b\sqrt{y})^{2}=a^{2}x-b^{2}y$ $\displaystyle \frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}} \displaystyle \color{red}{ \cdot\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}} }\qquad$ (rationalize) $ =\displaystyle \frac{\sqrt{a}(\sqrt{a}+\sqrt{b})}{(\sqrt{a})^{2}-(\sqrt{b})^{2}} =\frac{\sqrt{a}(\sqrt{a}+\sqrt{b})}{a-b} $ $=\displaystyle \frac{(\sqrt{a})^{2}+\sqrt{a}\cdot\sqrt{b}}{a-b}$ = $\displaystyle \frac{a+\sqrt{ab}}{a-b}$
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