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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. 153 (page 680)

In the following exercises, simplify each complex rational expression by writing it as division.
$\frac{\frac{c}{c^{2} + 5 c - 14}}{\frac{10}{c + 7}}$

Short Answer

Expert verified

The simplified expression is $\frac{c}{10 (c - 2)}$ .

Step by step solution

01

Step 1. Given Information.

We have:

$\frac{\frac{c}{c^{2} + 5 c - 14}}{\frac{10}{c + 7}}$

02

Step 2. Find the LCD of all fractions in complex rational expression.

The least common divisor (LCD) is $(c + 7) (c - 2)$ .

Multiply the numerator and denominator by the LCD:

$= \frac{(c + 7) (c - 2) \frac{c}{c^{2} + 5 c - 14}}{(c + 7) (c - 2) \frac{10}{c + 7}}$

03

Step 3. Simplify the expression.

Further, calculate:

$= \frac{(c + 7) (c - 2) \frac{c}{(c^{2} + 5 c - 14)}}{(c + 7) (c - 2) \frac{10}{(c + 7)}} = \frac{(c + 7) (c - 2) \frac{c}{(c^{2} + 7 c - 2 c - 14)}}{(c + 7) (c - 2) \frac{10}{(c + 7)}} = \frac{(c + 7) (c - 2) \frac{c}{(c (c + 7) - 2 (c + 7))}}{(c + 7) (c - 2) \frac{10}{(c + 7)}} = \frac{(c + 7) (c - 2) \frac{c}{(c + 7) (c - 2)}}{(c + 7) (c - 2) \frac{10}{(c + 7)}} = \frac{c}{10 (c - 2)}$

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Most popular questions from this chapter

In the following exercises, divide the rational expressions.

$\frac{\frac{3 b^{2} + 2 b - 8}{12 b + 18}}{\frac{3 b^{2} + 2 b - 8}{2 b^{2} - 7 b - 15}}$

In the following exercises, divide the rational expressions.

$\frac{10 + w}{w - 8} 梅 \frac{100 - w^{2}}{8 - w}$

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

In the following exercise, perform the indicated operation:

$\frac{3 d}{d + 2} + \frac{4}{d} - \frac{d + 8}{d^{2} + 2 d}$

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

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

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