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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. 38 (page 652)

In the following exercises, multiply the rational expressions. $\frac{72 m - 12 m^{2}}{8 m + 32} . \frac{m^{2} + 10 m + 24}{m^{2} - 36}$

Short Answer

Expert verified

The simplified answer is $\frac{- 3 m}{2} .$

Step by step solution

01

Step 1. Given Information

$\frac{72 m - 12 m^{2}}{8 m + 32} . \frac{m^{2} + 10 m + 24}{m^{2} - 36}$

02

Step 2. Factor each numerator and denominator completely.

$72 m - 12 m^{2} = 12 m (6 - m)$ and

$m^{2} + 10 m + 24 = (m + 6) (m + 4)$ and

$8 m + 32 = 8 (m + 4)$ and

$m^{2} - 36 = (m - 6) (m + 6)$

03

Step 3. Multiply the numerators and denominators.Simplify by dividing out common factors

$\frac{72 m - 12 m^{2}}{8 m + 32} . \frac{m^{2} + 10 m + 24}{m^{2} - 36} = \frac{12 m (6 - m)}{8 (m + 4)} . \frac{(m + 6) (m + 4)}{(m - 6) (m + 6)}$

\frac{- 12 m (m - 6)}{8 (m + 4)} . \frac{(m + 6) (m + 4)}{(m - 6) (m + 6)} = \frac{- 3 m}{2}

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Most popular questions from this chapter

Simplify the complex rational expression by writing it as division:

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