Chapter 8: Q. 297 (page 967)

Simplify
In the following exercises, use either method.
$\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}}$ .

Short Answer

Expert verified

The simplified expression for $\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}}$ is, $\frac{(x - 1) (x - 2)}{6}$ .

Step by step solution

Step 1. Given information

$\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}}$ .

We need to simplify the given expression.

Step 2.Find the LCD and add the fractions in the numerator.

Find the LCD and add the fractions in the denominator.

$\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}} = \frac{\frac{x (x + 2)}{x + 2} - \frac{3 x}{x + 2}}{\frac{3 (x - 2)}{(x - 2) (x + 2)} + \frac{3 (x + 2)}{(x + 2) (x - 2)}}$ .

Now simplify both the numerators and the denominators.

$\frac{\frac{x (x + 2)}{x + 2} - \frac{3 x}{x + 2}}{\frac{3 (x - 2)}{(x - 2) (x + 2)} + \frac{3 (x + 2)}{(x + 2) (x - 2)}} = \frac{\frac{(x^{2} + 2 x)}{x + 2} - \frac{3 x}{x + 2}}{\frac{(3 x - 6)}{(x - 2) (x + 2)} + \frac{(3 x + 6)}{(x + 2) (x - 2)}} = \frac{\frac{x^{2} + 2 x - 3 x}{x + 2}}{\frac{3 x - 6 + 3 x + 6}{(x - 2) (x + 2)}}$

Step 3. Now simplify the obtained expression

$\frac{\frac{x^{2} + 2 x - 3 x}{x + 2}}{\frac{3 x - 6 + 3 x + 6}{(x - 2) (x + 2)}} = \frac{\frac{x^{2} - x}{x + 2}}{\frac{6 x}{(x - 2) (x + 2)}} = \frac{x^{2} - x}{\frac{6 x}{(x - 2)}} = \frac{(x^{2} - x) (x - 2)}{6 x} = \frac{x (x - 1) (x - 2)}{6 x} = \frac{(x - 1) (x - 2)}{6}$

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Simplify
In the following exercises, use either method.
$\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2.Find the LCD and add the fractions in the numerator.

Step 3. Now simplify the obtained expression

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SimplifyIn the following exercises, use either method.x-3xx+23x+2+3x-2.

Short Answer

Step by step solution

Step 1. Given information

Step 2.Find the LCD and add the fractions in the numerator.

Step 3. Now simplify the obtained expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Calculus

Geometry

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Decision Maths

Study anywhere. Anytime. Across all devices.

Simplify
In the following exercises, use either method.
$\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}}$ .