Answer
$2(a - \sqrt{a^2-1})$
Work Step by Step
$f(\sqrt{a + 1} - \sqrt{a - 1})$
$=(\sqrt{a + 1} - \sqrt{a - 1})^2$
$=(\sqrt{a + 1})^2 + (\sqrt{a - 1})^2 - 2\sqrt{a + 1}\sqrt{a - 1}$
$=(a+1 + a - 1 - 2\sqrt{a^2-1}$
$= 2(a - \sqrt{a^2-1})$
Intermediate Algebra for College Students (7th Edition)
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13417-894-7
ISBN 13:
978-0-13417-894-3
Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 551: 116
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