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: 79



Work Step by Step

We lose the square roots in the denominator by applying the difference of squares formula: $(a\sqrt{x}+b\sqrt{y})(a\sqrt{x}-b\sqrt{y})=(a\sqrt{x})^{2}-(b\sqrt{y})^{2}=a^{2}x-b^{2}y$ $\displaystyle \frac{6}{\sqrt{5}+\sqrt{3}} \displaystyle \color{red}{ \cdot\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}} }\qquad$ (rationalize) $ =\displaystyle \frac{6(\sqrt{5}-\sqrt{3})}{(\sqrt{5})^{2}-(\sqrt{3})^{2}} =\frac{6(\sqrt{5}-\sqrt{3})}{5-3} =\frac{6(\sqrt{5}-\sqrt{3})}{2}$ $=3(\sqrt{5}-\sqrt{3})$ = $3\sqrt{5}-3\sqrt{3}$
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