Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Review: 110

Answer

$-5+2\sqrt{6}$

Work Step by Step

Multiplying by the conjugate of the denominator, the rationalized-denominator form of the given expression, $ \dfrac{\sqrt[]{2}-\sqrt{3}}{\sqrt[]{2}+\sqrt{3}} ,$ is \begin{array}{l}\require{cancel} \dfrac{\sqrt[]{2}-\sqrt{3}}{\sqrt[]{2}+\sqrt{3}}\cdot\dfrac{\sqrt[]{2}-\sqrt{3}}{\sqrt[]{2}-\sqrt{3}} \\\\= \dfrac{(\sqrt[]{2}-\sqrt{3})^2}{(\sqrt[]{2})^2-(\sqrt{3})^2} \\\\= \dfrac{(\sqrt[]{2})^2+2(\sqrt{2})(-\sqrt{3})+(-\sqrt{3})^2}{2-3} \\\\= \dfrac{2-2\sqrt{2(3)}+3}{-1} \\\\= \dfrac{5-2\sqrt{6}}{-1} \\\\= -5+2\sqrt{6} .\end{array}
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