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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 8: Q 618. (page 1030)

In the following exercises, perform the indicated operation and simplify.
$\frac{1}{z - 9} - \frac{3}{z + 9}$

Short Answer

Expert verified

The required answer is $\frac{- 2 z + 36}{(z - 9) (z + 9)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{1}{z - 9} - \frac{3}{z + 9}$

02

Step 2. Simplify the expression.

$\frac{1}{z - 9} - \frac{3}{z + 9}$

Find the LCD:

The LCD of $(z - 9) and (z + 9)$ is $(z - 9) (z + 9)$ ,

Rewrite each rational expression as an equivalent rational expression with the LCD,

$\frac{1 路 (z + 9)}{(z - 9) 路 (z + 9)} - \frac{3 路 (z - 9)}{(z + 9) 路 (z - 9)}$

Simplify,

$\frac{z + 9}{(z - 9) (z + 9)} - \frac{3 (z - 9)}{(z - 9) (z + 9)}$

Now subtract the rational expressions and simplify,

$\frac{z + 9 - 3 (z - 9)}{(z - 9) (z + 9)} \frac{z + 9 - 3 z + 27}{(z - 9) (z + 9)} \frac{- 2 z + 36}{(z - 9) (z + 9)}$

Therefore, the simplified value is $\frac{- 2 z + 36}{(z - 9) (z + 9)}$ .

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