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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q7.59TI. (page 677)

Simplify the complex rational expression by using the LCD:
$\frac{\frac{3}{x + 2}}{\frac{5}{x - 2} - \frac{3}{x^{2} - 4}}$

Short Answer

Expert verified

$\frac{3 x - 6}{5 x + 7}$

Step by step solution

01

Step 1. Given information.

The following complex rational expression is given:

$\frac{\frac{3}{x + 2}}{\frac{5}{x - 2} - \frac{3}{x^{2} - 4}}$

02

Step 2. Simplification of the complex rational expression.

The LCD of all the fractions the numerator and the denominator is $x^{2} - 4 = (x + 2) (x - 2)$ .

Multiplying both the numerator and the denominator by LCD:

$\frac{(x^{2} - 4) . \frac{3}{x + 2}}{(x^{2} - 4) . (\frac{5}{x - 2} - \frac{3}{x^{2} - 4})}$

Distributing and simplifying:

$\frac{(x + 2) (x - 2) . \frac{3}{x + 2}}{(x + 2) (x - 2) . \frac{5}{x - 2} - (x^{2} - 4) . \frac{3}{x^{2} - 4}} \frac{3 (x - 2)}{5 (x + 2) - 3}$

Simplifying:

$\frac{3 x - 6}{5 x + 7}$

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Most popular questions from this chapter

Determine the values for which the rational expression is undefined.

$\frac{5 a + 3}{3 a - 2}$

Simplify the complex rational expression by writing it as division:

$\frac{b - \frac{3 b}{b + 5}}{\frac{2}{b + 5} + \frac{1}{b - 5}}$

Simplify the complex rational expression by writing it as a division:

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

In the following exercise, find

(a) $R (x) = f (x) + g (x)$

(b) $R (x) = f (x) - g (x)$ :

role="math" localid="1644749808906" $f (x) = \frac{5}{x + 7} g (x) = \frac{10 x}{x^{2} - 49}$

Multiply $\frac{5}{8} . \frac{4}{15}$

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