Chapter 8: 538 - Review Exercises (page 1025)

Divide Rational Expressions
In the following exercises, divide.
$\frac{8 m^{2} - 8 m}{m - 4} . \frac{m^{2} + 2 m - 24}{m^{2} + 7 m + 10} \div \frac{2 m^{2} - 6 m}{m + 5} .$

Short Answer

Expert verified

The answer is $\frac{4 m^{2} - 20 m - 24}{m^{2} - m - 6} .$

Step by step solution

Step 1. Given Information.

$\frac{8 m^{2} - 8 m}{m - 4} . \frac{m^{2} + 2 m - 24}{m^{2} + 7 m + 10} \div \frac{2 m^{2} - 6 m}{m + 5}, = \frac{(\frac{8 m^{2} - 8 m}{m - 4}) \times (\frac{m^{2} + 2 m - 24}{m^{2} + 7 m + 10})}{\frac{2 m^{2} - 6 m}{m + 5}} .$

Step 2. Solving the numerator first.

$(\frac{8 m^{2} - 8 m}{m - 4}) \times (\frac{m^{2} + 2 m - 24}{m^{2} + 7 m + 10}) = (\frac{8 m (m - 1)}{m - 4}) \times (\frac{m^{2} + 2 m - 24}{m^{2} + 7 m + 10}) = (\frac{8 m (m - 1)}{m - 4}) \times (\frac{(m - 4) (m + 6)}{(m + 2) (m + 5)}) = \frac{8 m (m - 1) (m + 6)}{(m + 2) (m + 5)} .$

Step 3. Solving the rational expression.

$\frac{\frac{8 m (m - 1) (m + 6)}{(m + 2) (m + 5)}}{\frac{2 m (m - 3)}{(m + 5)}}, = \frac{8 m (m - 1) (m + 6) (m + 5)}{(m + 2) (m + 5) 2 m (m - 3)}, S o l v i n g a n d c a n c e l l i n g s a m e f a c t o r s, w e g e t, = \frac{4 (m - 1) (m + 6)}{(m + 2) (m - 3)} = \frac{4 m^{2} - 20 m - 24}{m^{2} - m - 6} .$

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Divide Rational Expressions
In the following exercises, divide.
$\frac{8 m^{2} - 8 m}{m - 4} . \frac{m^{2} + 2 m - 24}{m^{2} + 7 m + 10} \div \frac{2 m^{2} - 6 m}{m + 5} .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solving the numerator first.

Step 3. Solving the rational expression.

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Divide Rational ExpressionsIn the following exercises, divide.8m2-8mm-4.m2+2m-24m2+7m+10÷2m2-6mm+5.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solving the numerator first.

Step 3. Solving the rational expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Logic and Functions

Pure Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Divide Rational Expressions
In the following exercises, divide.
$\frac{8 m^{2} - 8 m}{m - 4} . \frac{m^{2} + 2 m - 24}{m^{2} + 7 m + 10} \div \frac{2 m^{2} - 6 m}{m + 5} .$