Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Integrated Review - Radicals and Rational Exponents: 37

Answer

$\frac{13-3\sqrt {21}}{5}$

Work Step by Step

$\frac{\sqrt 3-\sqrt 7}{2\sqrt 3+\sqrt 7}\times\frac{2\sqrt 3-\sqrt 7}{2\sqrt 3-\sqrt 7}$ =$\frac{(\sqrt 3-\sqrt 7)(2\sqrt 3-\sqrt 7)}{(2\sqrt 3+\sqrt 7)(2\sqrt 3-\sqrt 7)}$ =$\frac{\sqrt 3(2\sqrt 3-\sqrt 7)-\sqrt 7(2\sqrt 3-\sqrt 7)}{(2\sqrt 3)^{2}-(\sqrt 7)^{2}}$ =$\frac{2(3)-\sqrt 7\sqrt 3-2\sqrt 7\sqrt 3+7}{(2\sqrt 3)^{2}-(\sqrt 7)^{2}}$ =$\frac{6-\sqrt {21}-2\sqrt {21}+7}{4(3)-7}$ =$\frac{6+7+(-1-2)\sqrt {21}}{12-7}$ =$\frac{13-3\sqrt {21}}{5}$
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