Q. 7.42 Subtract: 4x2-4-3x2-x-2.... [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. 7.42 (page 664)

Subtract: $\frac{4}{x^{2} - 4} - \frac{3}{x^{2} - x - 2}$ .

Short Answer

Expert verified

The resultant expression is $\frac{1}{(x + 2) (x + 1)}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{4}{x^{2} - 4} - \frac{3}{x^{2} - x - 2}$ .

Step 2. Express with common denominator

Factor the denominators of the given expression.

$\frac{4}{(x - 2) (x + 2)} - \frac{3}{(x - 2) (x + 1)}$

The LCD of the terms of obtained expression is $(x - 2) (x + 2) (x + 1)$ .
Multiply the numerator and denominator of first term by $(x + 1)$ and second term by $(x + 2)$ .

$\frac{4 (x + 1)}{(x - 2) (x + 2) (x + 1)} - \frac{3 (x + 2)}{(x - 2) (x + 1) (x + 2)}$

Step 3. Simplify

As the denominator is the same for both the terms, subtract the numerator and place it over the common denominator.

$\frac{4 x + 4 - 3 x - 6}{(x - 2) (x + 2) (x + 1)} = \frac{x - 2}{(x - 2) (x + 2) (x + 1)}$

Cancel the common factors from numerator and denominator.

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

So, the resultant expression is localid="1645089873634">1(x+2)(x+1).

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91影视

Subtract: $\frac{4}{x^{2} - 4} - \frac{3}{x^{2} - x - 2}$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

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