# Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 551: 116

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

#### 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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