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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. 41 (page 652)

In the following exercises, multiply the rational expressions.
$\frac{6 m^{2} - 2 m - 10}{9 - m^{2}} . \frac{m^{2} - 6 m + 9}{6 m^{2} + 29 m - 20}$

Short Answer

Expert verified

The simplified expression is $\frac{- 2 (3 m^{2} - m - 5)}{(6 m^{2} + 29 m - 20)}$

Step by step solution

01

Step 1. Given expression

$\frac{6 m^{2} - 2 m - 10}{9 - m^{2}} . \frac{m^{2} - 6 m + 9}{6 m^{2} + 29 m - 20}$

We have to multiply the given rational expression.

02

Step 2. Factor the numerators and denominators

$\frac{6 m^{2} - 2 m - 10}{9 - m^{2}} . \frac{m^{2} - 6 m + 9}{6 m^{2} + 29 m - 20} = \frac{2 (3 m^{2} - m - 5)}{(3 - m) (3 + m)} . \frac{(m - 3) (m + 3)}{6 m^{2} + 29 m - 20} = \frac{2 (3 m^{2} - m - 5) (m - 3) (m + 3)}{- (m - 3) (3 + m) (6 m^{2} + 29 m - 20)}$

03

Step 3. Remove the common factors

$\frac{- 2 (3 m^{2} - m - 5)}{(6 m^{2} + 29 m - 20)} =$

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Most popular questions from this chapter

Solve the proportion $\frac{56}{72} = \frac{y}{9}$ .

Solve the proportion $\frac{z}{z - 84} = - \frac{1}{5}$ .

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.

$\frac{3 s^{2}}{s^{2} - 16} 梅 \frac{s^{3} - 4 s^{2} + 16 s}{s^{3} - 64}$

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$\frac{1}{x^{2} - 16} < 0$

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