Chapter 7: Q7.47TI (page 671)

Simplify the complex rational expression by writing it as a division:
$\frac{\frac{2}{x^{2} - 1}}{\frac{3}{x + 1}}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

The following complex rational expression is given:

$\frac{\frac{2}{x^{2} - 1}}{\frac{3}{x + 1}}$

Step 2. Simplification of the rational expression.

Rewrite the fraction as a division:

$\frac{2}{x^{2} - 1} \div \frac{3}{x + 1}$

Rewrite as the product of the first and the reciprocal of the second:

$\frac{2}{x^{2} - 1} . \frac{x + 1}{3}$

Factor the terms whenever possible:

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

Multiply:

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

Remove the common factors present in the numerator and the denominator:

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

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Simplify the complex rational expression by writing it as a division:
$\frac{\frac{2}{x^{2} - 1}}{\frac{3}{x + 1}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the rational expression.

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Simplify the complex rational expression by writing it as a division:2x2-13x+1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the rational expression.

One App. One Place for Learning.

Most popular questions from this chapter

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Simplify the complex rational expression by writing it as a division:
$\frac{\frac{2}{x^{2} - 1}}{\frac{3}{x + 1}}$