Answer
$ \frac{8\sqrt 5-19}{41}$
Work Step by Step
$\frac{2-\sqrt 5}{2+3\sqrt 5}=\frac{2-\sqrt 5}{2+3\sqrt 5}\times\frac{2-3\sqrt 5}{2-3\sqrt 5}=\frac{4-6\sqrt 5-2\sqrt 5+15}{4-45}=\frac{8\sqrt 5-19}{41}$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Appendix A - Review - A.7 nth Roots; Rational Exponents - A.7 Assess Your Understanding - Page A61: 49
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