College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 79: 58


$\displaystyle \frac{3(\sqrt{5}-4)}{11}=\frac{3\sqrt{5}-12}{11}$

Work Step by Step

We rationalize the denominator: $\displaystyle \frac{-3}{\sqrt{5}+4}=\frac{-3(\sqrt{5}-4)}{(\sqrt{5}+4)(\sqrt{5}-4)}=\frac{-3(\sqrt{5}-4)}{5-4^2}=\frac{-3(\sqrt{5}-4)}{-11}=\frac{3(\sqrt{5}-4)}{11}=\frac{3\sqrt{5}-12}{11}$
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