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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. 393 (page 735)

In the following exercise, divide.
$\frac{\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}}{\frac{c^{2} - 4 c - 32}{15 c + 10}}$

Short Answer

Expert verified

The simplified expression is $\frac{5}{c + 4}$

Step by step solution

01

Step 1. Given information

Expression is $\frac{\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}}{\frac{c^{2} - 4 c - 32}{15 c + 10}}$

02

Step 2. Rewrite the complex fraction as division

$(\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}) 梅 (\frac{c^{2} - 4 c - 32}{15 c + 10})$

03

Step 3. Rewrite as the product of first times the reciprocal of the second.

$(\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}) 脳 (\frac{15 c + 10}{c^{2} - 4 c - 32})$

04

Step 4. Factorize the denominator and numerator

$(\frac{(c - 8) (c + 8)}{3 c^{2} + 24 c + 2 c + 16}) 脳 (\frac{5 (3 c + 2)}{c^{2} - 8 c + 4 c - 32}) = (\frac{(c - 8) (c + 8)}{3 c (c + 8) + 2 (c + 8)}) 脳 (\frac{5 (3 c + 2)}{c (c - 8) + 4 (c - 8)}) = \frac{(c - 8) (c + 8)}{(3 c + 2) (c + 8)} 脳 \frac{5 (3 c + 2)}{(c - 8) (c + 4)}$

05

Step 5.Multiply and remove common factors

$\frac{5 (c - 8) (c + 8) (3 c + 2)}{(3 c + 2) (c + 8) (c - 8) (c + 4)} = \frac{5}{c + 4}$

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Most popular questions from this chapter

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

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

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

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

$f (x) = \frac{x^{2} - 2 x}{x^{2} + 6 x - 16} a n d g (x) = \frac{x^{2} - 64}{x^{2} - 8 x}$

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$\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} . \frac{n^{2} - 10 n + 25}{2 n^{2} - 13 n + 21}$

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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