Chapter 7: Q7.60TI. (page 677)

Simplify the complex rational expression by using the LCD:
$\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$

Short Answer

Expert verified

$\frac{x + 21}{6 x - 43}$

Step by step solution

Step 1. Given information.

The following complex rational expression is given:

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

Step 2. Simplification of the complex rational expression.

The LCD of the numerator and the denominator fractions is $x^{2} - 49 = (x + 7) (x - 7)$ .

Multiplying both the numerator and the denominator by LCD and distributing:

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

Simplifying:

$\frac{2 (x + 7) - (x - 7)}{6 (x - 7) - 1}$

Distributing and simplifying:

$\frac{2 x + 14 - x + 7}{6 x - 42 - 1} \frac{x + 21}{6 x - 43}$

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Simplify the complex rational expression by using the LCD:
$\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the complex rational expression.

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Simplify the complex rational expression by using the LCD:2x-7-1x+76x+7-1x2-49

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the complex rational expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify the complex rational expression by using the LCD:
$\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$