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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 47 (page 1069)

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

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

01

Step 1. Given Information

We have

\frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} 梅 \frac{p^{2} - q^{2}}{12} = \frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} 脳 \frac{12}{p^{2} - q^{2}}

02

Step 2. Factors the numerators and denominators

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

03

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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Most popular questions from this chapter

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