Chapter 7: Q. 54 (page 652)

In the following exercises, divide the rational expressions.
$\frac{\frac{4 d^{2} + 7 d - 2}{35 d + 10}}{\frac{d^{2} - 4}{7 d^{2} - 12 d - 4}}$

Short Answer

Expert verified

The simplified expression is $\frac{4 d - 1}{5} .$

Step by step solution

Step 1. Given Information

$\frac{\frac{4 d^{2} + 7 d - 2}{35 d + 10}}{\frac{d^{2} - 4}{7 d^{2} - 12 d - 4}} = \frac{4 d^{2} + 7 d - 2}{35 d + 10} \div \frac{d^{2} - 4}{7 d^{2} - 12 d - 4}$

Step 2. Rewrite as product of first times reciprocalof second.

$\frac{4 d^{2} + 7 d - 2}{35 d + 10} \div \frac{d^{2} - 4}{7 d^{2} - 12 d - 4} = \frac{4 d^{2} + 7 d - 2}{35 d + 10} \times \frac{7 d^{2} - 12 d - 4}{d^{2} - 4}$

Step 3. Factor the numerators and thedenominators, and then multiply.

$= \frac{(4 d - 1) (d + 2)}{5 (7 d + 2)} \times \frac{(d - 2) (7 d + 2)}{(d - 2) (d + 2)} = \frac{(4 d - 1) (d + 2) (d - 2) (7 d + 2)}{5 (7 d + 2) (d - 2) (d + 2)}$

Step 4. Simplify by dividing out common factors.

$= \frac{4 d - 1}{5}$

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In the following exercises, divide the rational expressions.
$\frac{\frac{4 d^{2} + 7 d - 2}{35 d + 10}}{\frac{d^{2} - 4}{7 d^{2} - 12 d - 4}}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Rewrite as product of first times reciprocalof second.

Step 3. Factor the numerators and thedenominators, and then multiply.

Step 4. Simplify by dividing out common factors.

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In the following exercises, divide the rational expressions.4d2+7d-235d+10d2-47d2-12d-4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Rewrite as product of first times reciprocalof second.

Step 3. Factor the numerators and thedenominators, and then multiply.

Step 4. 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

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, divide the rational expressions.
$\frac{\frac{4 d^{2} + 7 d - 2}{35 d + 10}}{\frac{d^{2} - 4}{7 d^{2} - 12 d - 4}}$