Answer
$-5-2\sqrt{5}$
Work Step by Step
Multiply using the conjugate. Remember that $(a^2-b^2)$ is $(a+b)(a-b)$
$\frac{\sqrt{5}}{2-\sqrt{5}}\cdot \frac{2+\sqrt{5}}{2+\sqrt{5}}=\frac{2\sqrt{5}+5}{4-5}=\frac{2\sqrt{5}+5}{-1}=-5-2\sqrt{5}$
Algebra 1
by Hall, Prentice
Published by
Prentice Hall
ISBN 10:
0133500403
ISBN 13:
978-0-13350-040-0
Chapter 10 - Radical Expressions and Equations - 10-3 Operations with Radial Expressions - Practice and Problem-Solving Exercises - Page 616: 33
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