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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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

01

Step 1. Given information.

The following complex rational expression is given:

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

02

Step 2. Simplification of the rational expression.

Rewrite the fraction as a division:

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

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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Most popular questions from this chapter

In the following exercises, multiply the rational expressions. $\frac{72 m - 12 m^{2}}{8 m + 32} . \frac{m^{2} + 10 m + 24}{m^{2} - 36}$

In the following exercises, divide the rational expressions.

$\frac{\frac{4 d^{2} + 7 d - 2}{35 d + 10}}{\frac{d^{2} - 4}{7 d^{2} - 12 d - 4}}$

In the following expression, perform the indicated operation:

$\frac{5 a}{a - 2} + \frac{9}{a} - \frac{2 a + 18}{a^{2} - 2 a}$

For the following exercises, perform the indicated operations. $\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} 梅 \frac{5 m^{2} + 10 m}{2 m - 10}$

Simplify $\frac{7 y - 35}{25 - y^{2}}$

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