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

Step 1. Given information.

The given expression is:

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

Step 2. Concepts.

The following concepts are required for simplification:

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

Step 3. Rewrite the expression and then simplify.

Rewrite the complex fraction as division.

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

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

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

Step 4. Conclusion.

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concepts.

Step 3. Rewrite the expression and then simplify.

Step 4. Conclusion.

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Simplify:2x2-13x+1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concepts.

Step 3. Rewrite the expression and then simplify.

Step 4. Conclusion.

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Most popular questions from this chapter

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