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: 55


$\displaystyle -\frac{19-8\sqrt{5}}{41}=\frac{8\sqrt{5}-19}{41}$

Work Step by Step

We rationalize the denominator: $\displaystyle \frac{2-\sqrt{5}}{2+3\sqrt{5}}=\frac{(2-\sqrt{5})(2-3\sqrt{5})}{(2+3\sqrt{5})(2-3\sqrt{5})}=\frac{(2-\sqrt{5})(2-3\sqrt{5})}{2^2-(3\sqrt{5})^2}=\frac{(2-\sqrt{5})(2-3\sqrt{5})}{4-9*5}=\frac{2*2-2*3\sqrt{5}-2\sqrt{5}+3\sqrt{5}\sqrt{5}}{-41}=\frac{4-6\sqrt{5}-2\sqrt{5}+3*5}{-41}=\frac{19-8\sqrt{5}}{-41}=\frac{8\sqrt{5}-19}{41}$
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