Chapter 11: Q.485. (page 1069)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

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

Step 2. Simplify the rational expression.

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

Step 3. Simplified answer.

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the rational expression.

Step 3. Simplified answer.

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Perform the indicated operation and simplify.4xx+2·x2+5x+612x2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the rational expression.

Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Decision Maths

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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