Chapter 7: Q. 45 (page 652)

In the following exercises, divide the rational expressions.
$\frac{3 s^{2}}{s^{2} - 16} \div \frac{s^{3} - 4 s^{2} + 16 s}{s^{3} - 64}$

Short Answer

Expert verified

The simplified expression is $\frac{3 s^{3}}{{(s - 4)}^{2} (s + 4)} .$

Step by step solution

Step 1. Given Information

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

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

Step 2. Factors the numerators and denominators

$\frac{3 s^{2}}{(s - 4) (s + 4)} \times \frac{s (s^{2} - 4 s + 16)}{s^{3} - 4^{3}} = \frac{3 s^{2}}{(s - 4) (s + 4)} \times \frac{s (s^{2} - 4 s + 16)}{(s - 4) (s^{2} - 4 s + 16)}$

Step 3. Multiply numerators and denominators and remove common factors

$= \frac{3 s \times s}{(s - 4) (s + 4)} \times \frac{s (s^{2} - 4 s + 16)}{(s - 4) (s^{2} - 4 s + 16)} = \frac{3 s^{3}}{{(s - 4)}^{2} (s + 4)}$

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In the following exercises, divide the rational expressions.
$\frac{3 s^{2}}{s^{2} - 16} \div \frac{s^{3} - 4 s^{2} + 16 s}{s^{3} - 64}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factors the numerators and denominators

Step 3. Multiply numerators and denominators and remove common factors

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In the following exercises, divide the rational expressions.3s2s2-16÷s3-4s2+16ss3-64

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factors the numerators and denominators

Step 3. Multiply numerators and denominators and remove common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Decision Maths

Discrete Mathematics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, divide the rational expressions.
$\frac{3 s^{2}}{s^{2} - 16} \div \frac{s^{3} - 4 s^{2} + 16 s}{s^{3} - 64}$