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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 175 (page 680)

In the following exercises, simplify each complex rational expression by using the LCD.
$\frac{\frac{2}{x + 5}}{\frac{3}{x - 5} + \frac{1}{x^{2} - 25}}$

Short Answer

Expert verified

The simplified expression is $\frac{2 (x - 5)}{3 x + 16}$ .

Step by step solution

01

Step 1. Given Information.

We have:

$\frac{\frac{2}{x + 5}}{\frac{3}{x - 5} + \frac{1}{x^{2} - 25}}$

02

Step 2. Multiply the numerator and denominator by the LCD.

The least common divisor (LCD) is $(x - 5) (x + 5)$ .

Multiply the numerator and denominator by $(x - 5) (x + 5)$ :

$= \frac{(x - 5) (x + 5) (\frac{2}{x + 5})}{(x - 5) (x + 5) (\frac{3}{x - 5} + \frac{1}{x^{2} - 25})}$

03

Step 3. Simplify the expression.

We have:

$= \frac{(x - 5) (x + 5) (\frac{2}{x + 5})}{(x - 5) (x + 5) (\frac{3}{x - 5} + \frac{1}{x^{2} - 5^{2}})} = \frac{(x - 5) (x + 5) (\frac{2}{x + 5})}{(x - 5) (x + 5) (\frac{3}{x - 5} + \frac{1}{(x - 5) (x + 5)})} = \frac{(x - 5) (x + 5) (\frac{2}{x + 5})}{(x - 5) (x + 5) \frac{3}{x - 5} + (x - 5) (x + 5) \frac{1}{(x - 5) (x + 5)}} = \frac{2 (x + 5)}{3 (x + 5) + 1} = \frac{2 x + 10}{3 x + 15 + 1} = \frac{2 x + 10}{3 x + 16} = \frac{2 (x - 5)}{3 x + 16}$

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Most popular questions from this chapter

For the following exercises, perform the indicated operations.
$\frac{12 p^{2} + 3 p}{p + 3} 梅 \frac{p^{2} + 2 p - 63}{p^{2} - p - 12} . \frac{p - 7}{9 p^{3} - 9 p^{2}}$

Solve the rational equation $\frac{E}{c} = m^{2}$ for the variable c.

Solve each rational function inequality and write the solution in interval notation.

Given the function $R (x) = \frac{(x + 1)}{(x + 3)}$ , find the values of x that make the function less than or equal to 0.

Solve the proportion $\frac{x}{56} = \frac{7}{8}$ .

If $a$ varies directly as $b$ and $a = 16$ , when $b = 4$ . Find the equation that relates $a$ and $b$ .

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