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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 8.99 (page 957)

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

Short Answer

Expert verified

The simplified form of the given expression is $\frac{2}{3 (x - 1)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

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

02

Step 2. Concepts.

The following concepts are required for simplification:

$\begin{array}{rcl} \frac{A}{B} 梅 \frac{C}{D} & = & \frac{A}{B} 路 \frac{D}{C} \\ a^{2} - b^{2} & = & (a - b) (a + b) \end{array}$

03

Step 3. Rewrite the expression and then simplify.

Rewrite the complex fraction as division.

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

Rewrite as the product of first times the reciprocal of the second.

$= \frac{2}{x^{2} - 1} 路 \frac{x + 1}{3} = \frac{2}{(x - 1) (x + 1)} 路 \frac{x + 1}{3} = \frac{2 (x + 1)}{3 (x - 1) (x + 1)} = \frac{2}{3 (x - 1)}$

04

Step 4. Conclusion.

The simplified form of the given expression is $\frac{2}{3 (x - 1)}$ .

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Most popular questions from this chapter

Efraim wants to start simplifying the complex fraction $\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a} - \frac{1}{b}}$ by cancelling the variables from the numerator and denominator. Explain what is wrong with Efraim鈥檚 plan.

In the following exercises, simplify.

$\frac{x^{2} + 4 x - 5}{x^{2} - 2 x + 1}$

In the following exercises, simplify.

$\frac{\frac{2}{3} - \frac{1}{9}}{\frac{3}{4} + \frac{5}{6}}$

In the following exercises, solve.

$\frac{6}{3} - \frac{2}{d} = \frac{4}{9}$

In the following exercises, solve.

$1 + \frac{9}{p} = \frac{- 20}{p^{2}}$

See all solutions

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