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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 8.91 (page 949)

Subtract : $\frac{2 x}{x^{2} - 4} - \frac{1}{x + 2}$ .

Short Answer

Expert verified

The subtraction of the rational expression is $\frac{1}{x - 2}$

Step by step solution

01

Given information

The given rational expression is $\frac{2 x}{x^{2} - 4} - \frac{1}{x + 2}$ .

02

Simplification of the expression

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

The LCD of the expression is $(x + 2) (x - 2)$ .

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

$= \frac{2 x}{(x + 2) (x - 2)} - \frac{1 脳 (x - 2)}{(x + 2) 脳 (x - 2)} S i m p l i f y t h e n u m e r a t o r s$

localid="1648230428307" $= \frac{2 x}{(x + 2) (x - 2)} - \frac{(x - 2)}{(x + 2) (x - 2)} = \frac{2 x - (x - 2)}{(x + 2) (x - 2)} = \frac{2 x - x + 2}{(x + 2) (x - 2)} = \frac{x + 2}{(x + 2) (x - 2)} S i m p l i f y \frac{1}{x - 2}$

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