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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 99 (page 1069)

In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator.
$\frac{5}{x^{2} - 2 x - 8}, \frac{2 x}{x^{2} - x - 12}$

Short Answer

Expert verified

(a) The LCD is $(x + 2) (x + 3) (x - 4)$ .

(b) The expressions with LCD are $\frac{5 (x + 3)}{(x + 2) (x + 3) (x - 4)}, \frac{2 x (x + 2)}{(x + 2) (x + 3) (x - 4)}$ .

Step by step solution

01

Part (a) Step 1. Given Information

The given expressions are $\frac{5}{x^{2} - 2 x - 8}, \frac{2 x}{x^{2} - x - 12}$

02

Part (a) Step 2. Find LCD

Factor the denominators of both the given rational expressions.

$x^{2} - 2 x - 8 = (x - 4) (x + 2) x^{2} - x - 12 = (x - 4) (x + 3)$

So, the LCD is $(x + 2) (x + 3) (x - 4)$ .

03

Part (b) Step 1. Given Information

The given expressions are $\frac{5}{x^{2} - 2 x - 8}, \frac{2 x}{x^{2} - x - 12}$ .

04

Part (b) Step 2. Express the expressions with LCD

Multiply and divide the expressions by the missing factor to make the denominator equal to LCD.

$\frac{5}{x^{2} - 2 x - 8} = \frac{5 (x + 3)}{(x + 2) (x + 3) (x - 4)} \frac{2 x}{x^{2} - x - 12} = \frac{2 x (x + 2)}{(x + 2) (x + 3) (x - 4)}$

So, the expressions with equal denominators arelocalid="1645165348019">5x+3x+2x+3x-4,2xx+2x+2x+3x-4.

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