Algebra: A Combined Approach (4th Edition)

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

Chapter 10 - Review: 110


$-5+2\sqrt {6}$

Work Step by Step

$\frac{\sqrt 2-\sqrt 3}{\sqrt 2+\sqrt 3}\times\frac{\sqrt 2-\sqrt 3}{\sqrt 2-\sqrt 3}$ =$\frac{(\sqrt 2-\sqrt 3)(\sqrt 2-\sqrt 3)}{(\sqrt 2-\sqrt 3)(\sqrt 2+\sqrt 3)}$ =$\frac{\sqrt 2(\sqrt 2-\sqrt 3)-\sqrt 3(\sqrt 2-\sqrt 3)}{(\sqrt 2)^{2}-(\sqrt 3)^{2}}$ =$\frac{\sqrt 2\sqrt 2-\sqrt 2\sqrt 3-\sqrt 2\sqrt 3+\sqrt 3\sqrt 3}{2-3}$ =$\frac{2-\sqrt {2\times3}-\sqrt {2\times3}+3}{-1}$ =$\frac{2-\sqrt {6}-\sqrt {6}+3}{-1}$ =$\frac{5-2\sqrt {6}}{-1}$ =$-5+2\sqrt {6}$
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