Q. 193 In the following exercises, simp... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 193 (page 681)

In the following exercises, simplify each complex rational expression using either method.
$\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}}$

Short Answer

Expert verified

The simplified form is $\frac{x^{2} - 3 x + 2}{6}$ .

Step by step solution

Step 1. Given.

The given complex rational expression is: $\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}}$ .

Step 2. To find

We have to simplify each complex rational expression by using either method.

Step 3. Calculation

LCM of the denominators is = $(x + 2) (x - 2)$ . Multiply numerator and denominator by it to simplify.

$\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}} = \frac{x (x + 2) (x - 2) - \frac{3 x}{x + 2} (x + 2) (x - 2)}{\frac{3}{x + 2} (x + 2) (x - 2) + \frac{3}{x - 2} (x + 2) (x - 2)} = \frac{x (x^{2} - 4) - 3 x (x - 2)}{3 (x - 2) + 3 (x + 2)} = \frac{x^{3} - 4 x - 3 x^{2} + 6 x}{3 x - 6 + 3 x + 6} = \frac{x^{3} - 3 x^{2} + 2 x}{6 x} = \frac{x (x^{2} - 3 x + 2)}{6 x} = \frac{x^{2} - 3 x + 2}{6}$

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91影视

In the following exercises, simplify each complex rational expression using 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.

Step 2. To find

Step 3. Calculation

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91影视

In the following exercises, simplify each complex rational expression using either method.x-3xx+23x+2+3x-2

Short Answer

Step by step solution

Step 1. Given.

Step 2. To find

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each complex rational expression using either method.
$\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}}$