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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 364 (page 1091)

In the following exercises, simplify by rationalizing the denominator
(a) $\frac{4}{4 + \sqrt{7}}$ (b) $\frac{7}{2 - \sqrt{6}}$

Short Answer

Expert verified

(a) $\frac{4 (4 - \sqrt{7})}{9}$

(b) $- \frac{7 (2 + \sqrt{6})}{2}$

Step by step solution

01

Step 1. Given Information

(a) $\frac{4}{4 + \sqrt{7}}$ (b) $\frac{7}{2 - \sqrt{6}}$

02

Part (a) of Step 1. Rationalize

$\frac{4}{4 + \sqrt{7}} \frac{4}{4 + \sqrt{7}} 脳 \frac{4 - \sqrt{7}}{4 - \sqrt{7}} \frac{4 (4 - \sqrt{7})}{(4 + \sqrt{7}) (4 - \sqrt{7})} \frac{4 (4 - \sqrt{7})}{9}$

03

Part (b) of Step 1. Rationalize

$\frac{7}{2 - \sqrt{6}} \frac{7}{2 - \sqrt{6}} 脳 \frac{2 + \sqrt{6}}{2 + \sqrt{6}} \frac{7 (2 + \sqrt{6})}{(2 - \sqrt{6}) (2 + \sqrt{6})} - \frac{7 (2 + \sqrt{6})}{2}$

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