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: 55


$\frac{2}{3(\sqrt 5-\sqrt 3)}=\frac{2}{3\sqrt 5-3\sqrt 3}$

Work Step by Step

$\frac{\sqrt 5+\sqrt 3}{3}=\frac{\sqrt 5+\sqrt 3}{3}\frac{\sqrt 5-\sqrt 3}{\sqrt 5-\sqrt 3}=\frac{\sqrt 5\sqrt 5-\sqrt 5\sqrt 3+\sqrt 3\sqrt 5-\sqrt 3\sqrt 3}{3(\sqrt 5-\sqrt 3)}=\frac{(\sqrt 5)^2-(\sqrt 3)^2}{3(\sqrt 5-\sqrt 3)}=\frac{5-3}{3(\sqrt 5-\sqrt 3)}=\frac{2}{3(\sqrt 5-\sqrt 3)}$
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