Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.3 - Radicals and Rational Exponents - Exercise Set - Page 45: 53

Answer

$3(\sqrt{5}-\sqrt{3})$

Work Step by Step

Use $(a+b)(a-b)=a^{2}-b^{2}\quad$ when rationalizing. $[(a+\sqrt{b})(a-\sqrt{b})=a^{2}-b]$ $\displaystyle \frac{6}{\sqrt{5}+\sqrt{3}}\cdot\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{6(\sqrt{5}-\sqrt{3})}{5-3}=$ $=\displaystyle \frac{6(\sqrt{5}-\sqrt{3})}{2}=3(\sqrt{5}-\sqrt{3})$
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