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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.485. (page 1069)

Perform the indicated operation and simplify.
$\frac{4 x}{x + 2} 路 \frac{x^{2} + 5 x + 6}{12 x^{2}}$

Short Answer

Expert verified

The solution is $\frac{x + 3}{3 x}$ .

Step by step solution

01

Step 1. Given information.

The given rational expression is:
$\frac{4 x}{x + 2} 路 \frac{x^{2} + 5 x + 6}{12 x^{2}}$

02

Step 2. Simplify the rational expression.

$\frac{4 x}{x + 2} 路 \frac{x^{2} + 5 x + 6}{12 x^{2}} = \frac{4 x}{x + 2} 路 \frac{x^{2} + 3 x + 2 x + 6}{12 x^{2}} \frac{4 x}{x + 2} 路 \frac{x^{2} + 5 x + 6}{12 x^{2}} = \frac{4 x}{x + 2} 路 \frac{x (x + 3) + 2 (x + 3)}{12 x^{2}} \frac{4 x}{x + 2} 路 \frac{x^{2} + 5 x + 6}{12 x^{2}} = \frac{4 x}{x + 2} 路 \frac{(x + 3) (x + 2)}{4 路 3 路 x^{2}} \frac{4 x}{x + 2} 路 \frac{x^{2} + 5 x + 6}{12 x^{2}} = \frac{x + 3}{3 x}$

03

Step 3. Simplified answer.

Hence, the simplified rational expression is $\frac{x + 3}{3 x}$ .

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