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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. 192 (page 681)

In the following exercises, simplify each complex rational expression using either method.
$\frac{\frac{2}{r - 9}}{\frac{1}{r + 9} + \frac{3}{r^{2} - 81}}$ .

Short Answer

Expert verified

The simplified form is $\frac{2 r + 18}{r - 6}$ .

Step by step solution

01

Step 1. Given.

The given complex rational expression is: $\frac{\frac{2}{r - 9}}{\frac{1}{r + 9} + \frac{3}{r^{2} - 81}}$ .

02

Step 2. To find

We have to simplify each complex rational expression by using either method.

03

Step 3. Calculation

LCM of the denominators is = $(r + 9) (r - 9)$ . Multiply numerator and denominator by it to simplify.

$\frac{\frac{2}{r - 9}}{\frac{1}{r + 9} + \frac{3}{r^{2} - 81}} = \frac{\frac{2}{r - 9} (r + 9) (r - 9)}{\frac{1}{r + 9} (r + 9) (r - 9) + \frac{3}{r^{2} - 81} (r + 9) (r - 9)} = \frac{2 (r + 9)}{(r - 9) + 3} = \frac{2 r + 18}{r - 9 + 3} = \frac{2 r + 18}{r - 6}$

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Most popular questions from this chapter

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{4}{x^{2} - 25} > 0$

Simplify $\frac{18}{24} .$

Simplify the complex rational expression by writing it as division:

$\frac{\frac{1}{x^{2} - 7 x + 12}}{\frac{2}{x - 4}}$

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

In the following exercises, divide the rational expressions.

$\frac{\frac{12 c^{2} - 12}{2 c^{2} - 3 c + 1}}{\frac{4 c + 4}{6 c^{2} - 13 c + 5}}$

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