Chapter 7: Q7.59TI. (page 677)

Simplify the complex rational expression by using the LCD:
$\frac{\frac{3}{x + 2}}{\frac{5}{x - 2} - \frac{3}{x^{2} - 4}}$

Short Answer

Expert verified

$\frac{3 x - 6}{5 x + 7}$

Step by step solution

Step 1. Given information.

The following complex rational expression is given:

$\frac{\frac{3}{x + 2}}{\frac{5}{x - 2} - \frac{3}{x^{2} - 4}}$

Step 2. Simplification of the complex rational expression.

The LCD of all the fractions the numerator and the denominator is $x^{2} - 4 = (x + 2) (x - 2)$ .

Multiplying both the numerator and the denominator by LCD:

$\frac{(x^{2} - 4) . \frac{3}{x + 2}}{(x^{2} - 4) . (\frac{5}{x - 2} - \frac{3}{x^{2} - 4})}$

Distributing and simplifying:

$\frac{(x + 2) (x - 2) . \frac{3}{x + 2}}{(x + 2) (x - 2) . \frac{5}{x - 2} - (x^{2} - 4) . \frac{3}{x^{2} - 4}} \frac{3 (x - 2)}{5 (x + 2) - 3}$

Simplifying:

$\frac{3 x - 6}{5 x + 7}$

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Simplify the complex rational expression by using the LCD:
$\frac{\frac{3}{x + 2}}{\frac{5}{x - 2} - \frac{3}{x^{2} - 4}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the complex rational expression.

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Simplify the complex rational expression by using the LCD:3x+25x-2-3x2-4

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the complex rational expression.

One App. One Place for Learning.

Most popular questions from this chapter

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Theoretical and Mathematical Physics

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Simplify the complex rational expression by using the LCD:
$\frac{\frac{3}{x + 2}}{\frac{5}{x - 2} - \frac{3}{x^{2} - 4}}$