#### Answer

$2(a - \sqrt{a^2-1})$

#### Work Step by Step

$f(\sqrt{a + 1} - \sqrt{a - 1})$
$=(\sqrt{a + 1} - \sqrt{a - 1})^2$
$=(\sqrt{a + 1})^2 + (\sqrt{a - 1})^2 - 2\sqrt{a + 1}\sqrt{a - 1}$
$=(a+1 + a - 1 - 2\sqrt{a^2-1}$
$= 2(a - \sqrt{a^2-1})$

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Published by
Pearson

ISBN 10:
0-13417-894-7

ISBN 13:
978-0-13417-894-3

$2(a - \sqrt{a^2-1})$

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