Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Prerequisites - P.2 - Exponents and Radicals - Exercises - Page 25: 53


$\frac{\sqrt {14}+2}{2}$

Work Step by Step

$\frac{5}{\sqrt {14}-2}=\frac{5}{\sqrt {14}-2}\frac{\sqrt {14}+2}{\sqrt {14}+2}=\frac{5\sqrt {14}+5\times2}{\sqrt {14}\sqrt {14}+\sqrt {14}(2)-2\sqrt {14}-2\times2}=\frac{5\sqrt {14}+10}{(\sqrt {14})^2-4}=\frac{5\sqrt {14}+10}{14-4}=\frac{5\sqrt {14}+10}{10}=\frac{5(\sqrt {14}+2)}{5\times2}=\frac{\sqrt {14}+2}{2}$
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