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

Step 1. Given Information

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

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

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

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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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

Step by step solution

Step 1. Given Information

Step 2. Factor each numerator and denominator completely.

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

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In the following exercises, multiply the rational expressions.72m-12m28m+32.m2+10m+24m2-36

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor each numerator and denominator completely.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Discrete Mathematics

Pure Maths

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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