Chapter 7: Q. 57 (page 653)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given Information

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

Step 2. Factor the numerators and denominators

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

Step 3. Remove the common factors

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

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the numerators and denominators

Step 3. Remove the common factors

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For the following exercises, perform the indicated operations.12p2+3pp+3÷p2+2p-63p2-p-12.p-79p3-9p2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor 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

Mechanics Maths

Calculus

Geometry

Probability and Statistics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

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