Answered: simplify x + 2 61. 62. x + 2 -E-

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.3: Rules For Addition

Problem 29WE

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Expert Solution

Step 1

(61)

Consider the given expression as

$\frac{1 + \frac{1}{x + 2}}{1 - \frac{1}{x + 2}}$

Step 2

Simplify as

$\begin{array}{rcl} \frac{1 + \frac{1}{x + 2}}{1 - \frac{1}{x + 2}} & = & \frac{\frac{x + 2 + 1}{x + 2}}{\frac{x + 2 - 1}{x + 2}} \\ = & \frac{\frac{x + 3}{x + 2}}{\frac{x + 1}{x + 2}} \\ = & \frac{(x + 3) (x + 2)}{(x + 1) (x + 2)} \\ = & \frac{x + 3}{x + 1} \end{array}$