College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.3: 52

Answer

$\frac{5 ( \sqrt3 + 1)}{2}$ or $\frac{5\sqrt3 + 5}{2}$

Work Step by Step

$ \frac{5}{(\sqrt 3 -1)}$ The conjugate of the denominator is $ \sqrt 3 + 1$. Multiply the denominator and numerator by $ \sqrt 3 + 1 $, so the simplified denominator will not contain a radical. Therefore, multiply by 1, choosing $\frac{ \sqrt 3 + 1}{ \sqrt 3 + 1}$ for 1. = $ \frac{5}{(\sqrt 3 -1)}$ $ \times $ $ \frac{\sqrt 3 + 1}{(\sqrt 3+1)}$ = $ \frac{5 ( \sqrt 3 + 1 )}{ ( \sqrt 3 - 1 ) ( \sqrt 3 + 1 )}$ $( \sqrt a - \sqrt b)( \sqrt a + \sqrt b)$ = $ (\sqrt a)^{2}$ - $ (\sqrt b)^{2}$. Therefore, $( \sqrt 3 - 1)( \sqrt3 + 1)$ = $ (\sqrt 3)^{2}$ - $ (1)^{2}$. = $ \frac{5 ( \sqrt 3 + 1 )}{ (\sqrt 3)^{2} - (1)^{2}}$ = $ \frac{5 ( \sqrt 3 + 1 )}{ 3 - 1}$ = $ \frac{5 ( \sqrt 3 + 1 )}{2}$ or $\frac{5\sqrt3 + 5}{2}$
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