Chapter 7: Q. 7.61 (page 678)

Simplify the complex rational expression by using the LCD:
$\frac{\frac{x^{2}}{x^{2} + 7 x + 10}}{\frac{4}{x + 2} + \frac{1}{x + 5}}$

Short Answer

Expert verified

The simplified expression is $\frac{x^{2}}{5 x + 22}$ .

Step by step solution

Step 1. Given Information.

We have:

$\frac{\frac{x^{2}}{x^{2} + 7 x + 10}}{\frac{4}{x + 2} + \frac{1}{x + 5}}$

Step 2. Find the LCD of all fractions in complex rational expression.

The least common divisor is $(x + 2) (x + 5) .$

Multiply the numerator and denominator by the LCD:

$= \frac{(x + 2) (x + 5) (\frac{x^{2}}{x^{2} + 7 x + 10})}{(x + 2) (x + 5) (\frac{4}{x + 2} + \frac{1}{x + 5})}$

Step 3. Simplify the expression.

Further, calculate:

$= \frac{(x + 2) (x + 5) (\frac{x^{2}}{x^{2} + 5 x + 2 x + 10})}{(x + 2) (x + 5) (\frac{4 (x + 5) + 1 (x + 2)}{(x + 2) (x + 5)})} = \frac{(x + 2) (x + 5) (\frac{x^{2}}{x (x + 5) + 2 (x + 5)})}{(x + 2) (x + 5) (\frac{4 (x + 5) + 1 (x + 2)}{(x + 2) (x + 5)})} = \frac{(x + 2) (x + 5) (\frac{x^{2}}{(x + 5) (x + 2)})}{(x + 2) (x + 5) (\frac{4 (x + 5) + 1 (x + 2)}{(x + 2) (x + 5)})} = \frac{x^{2}}{4 x + 20 + x + 2} = \frac{x^{2}}{5 x + 22}$

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Simplify the complex rational expression by using the LCD:
$\frac{\frac{x^{2}}{x^{2} + 7 x + 10}}{\frac{4}{x + 2} + \frac{1}{x + 5}}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the LCD of all fractions in complex rational expression.

Step 3. Simplify the expression.

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Simplify the complex rational expression by using the LCD:x2x2+7x+104x+2+1x+5

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the LCD of all fractions in complex rational expression.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Simplify the complex rational expression by using the LCD:
$\frac{\frac{x^{2}}{x^{2} + 7 x + 10}}{\frac{4}{x + 2} + \frac{1}{x + 5}}$