Chapter 8: Q. 8112 (page 963)

Simplify: $\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{x + 21}{6 x - 43}$ .

Step by step solution

Step 1. Given information.

The given expression is:

$\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$

Step 2. Rewrite the expression and then simplify.

The LCD of all the fractions in the whole expression is $(x - 7) (x + 7)$ . Clear the fractions by multiplying the numerator and denominator by that LCD.

role="math" localid="1647868522372" $= \frac{(x - 7) (x + 7) \cdot (\frac{2}{x - 7} - \frac{1}{x + 7})}{(x - 7) (x + 7) \cdot (\frac{6}{x + 7} - \frac{1}{x^{2} - 49})} = \frac{(x - 7) (x + 7) \cdot \frac{2}{x - 7} - (x - 7) (x + 7) \cdot \frac{1}{x + 7}}{(x - 7) (x + 7) \cdot \frac{6}{x + 7} - (x - 7) (x + 7) \cdot \frac{1}{(x - 7) (x + 7)}} = \frac{2 (x + 7) - (x - 7)}{6 (x - 7) - 1} = \frac{2 x + 14 - x + 7}{6 x - 42 - 1} = \frac{x + 21}{6 x - 43}$

Step 3. Conclusion.

The simplified form of the given expression is $\frac{x + 21}{6 x - 43}$ .

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Simplify: $\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the expression and then simplify.

Step 3. Conclusion.

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Simplify:2x-7-1x+76x+7-1x2-49

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the expression and then simplify.

Step 3. Conclusion.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Logic and Functions

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify: $\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$