Chapter 11: Q. 47 (page 1069)

In the following exercises, divide the rational expressions.
$\frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} \div \frac{p^{2} - q^{2}}{12}$

Short Answer

Expert verified

The simplified rational expression is $\frac{4 (p^{2} - p q + q^{2})}{(p^{2} + p q + q^{2}) (p - q)}$

Step by step solution

Step 1. Given Information

We have

\frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} \div \frac{p^{2} - q^{2}}{12} = \frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} \times \frac{12}{p^{2} - q^{2}}

Step 2. Factors the numerators and denominators

$\frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} \times \frac{12}{p^{2} - q^{2}} = \frac{(p + q) (p^{2} - p q + q^{2})}{3 (p^{2} + p q + q^{2})} \times \frac{12}{(p - q) (p + q)} = \frac{12 (p + q) (p^{2} - p q + q^{2})}{3 (p^{2} + p q + q^{2}) (p - q) (p + q)}$

Step 3. Remove the common factors

$\frac{4 (p^{2} - p q + q^{2})}{(p^{2} + p q + q^{2}) (p - q)}$

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In the following exercises, divide the rational expressions.
$\frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} \div \frac{p^{2} - q^{2}}{12}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factors the numerators and denominators

Step 3. Remove the common factors

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In the following exercises, divide the rational expressions.p3+q33p2+3pq+3q2÷p2-q212

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factors the numerators and denominators

Step 3. Remove the common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, divide the rational expressions.
$\frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} \div \frac{p^{2} - q^{2}}{12}$