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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 57 (page 653)

For the following exercises, perform the indicated operations.
$\frac{12 p^{2} + 3 p}{p + 3} 梅 \frac{p^{2} + 2 p - 63}{p^{2} - p - 12} . \frac{p - 7}{9 p^{3} - 9 p^{2}}$

Short Answer

Expert verified

The simplified expression is $\frac{(4 p + 1) (p - 4)}{3 p (p + 9) (p - 1)} .$

Step by step solution

01

Step 1. Given Information

$\frac{12 p^{2} + 3 p}{p + 3} 梅 \frac{p^{2} + 2 p - 63}{p^{2} - p - 12} . \frac{p - 7}{9 p^{3} - 9 p^{2}} = \frac{12 p^{2} + 3 p}{p + 3} . \frac{p^{2} - p - 12}{p^{2} + 2 p - 63} . \frac{p - 7}{9 p^{3} - 9 p^{2}}$

02

Step 2. Factor the numerators and denominators

$\frac{3 p (4 p + 1)}{p + 3} . \frac{(p - 4) (p + 3)}{(p + 9) (p - 7)} . \frac{p - 7}{9 p^{2} (p - 1)}$

03

Step 3. Remove the common factors

$= \frac{3 p (4 p + 1) (p - 4) (p + 3) (p - 7)}{9 p 脳 p (p + 3) (p + 9) (p - 7) (p - 1)} = \frac{(4 p + 1) (p - 4)}{3 p (p + 9) (p - 1)}$

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