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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q7.60TI. (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

01

Step 1. Given information.

The following complex rational expression is given:

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

02

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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Most popular questions from this chapter

In the following exercises, find the domain of each function.

$R (x) = \frac{x^{3} + 3 x^{2} - 4 x - 12}{x^{2} - 4}$

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

Solve the rational equation $\frac{3}{x} - \frac{5}{y} = \frac{1}{4}$ for the variable y.

For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.

$f (x) = \frac{2 x^{2} + 8 x}{x^{2} - 9 x + 20} a n d g (x) = \frac{x - 5}{x^{2}}$

Determine the values for which the rational expression is undefined.

$\frac{5 x^{2} y^{2}}{8 y}$

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