Chapter 8: Q 94. (page 930)

In the following exercises, multiply.
$\frac{6 p^{2} - 6 p}{p^{2} + 7 p - 18} \cdot \frac{p^{2} - 81}{3 p^{2} - 27 p}$

Short Answer

Expert verified

The required answer is $\frac{2 (p - 1)}{p - 2}$ .

Step by step solution

Step 1. Given information.

The given expression is:

$\frac{6 p^{2} - 6 p}{p^{2} + 7 p - 18} \cdot \frac{p^{2} - 81}{3 p^{2} - 27 p}$

Step 2. Simplify the expression.

$\frac{6 p^{2} - 6 p}{p^{2} + 7 p - 18} \cdot \frac{p^{2} - 81}{3 p^{2} - 27 p}$

Factor the numerator and denominator completely,

$\frac{6 p (p - 1)}{(p + 9) (p - 2)} \cdot \frac{(p + 9) (p - 2)}{3 p (p - 9)}$

Multiply the numerators and denominators,

$\frac{2 \cdot 3 p (p - 1) (p + 9) (p - 2)}{3 p (p + 9) (p - 2) (p - 9)}$

Simplify by dividing out common factors,

$\frac{2 (p - 1)}{p - 2}$

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In the following exercises, multiply.
$\frac{6 p^{2} - 6 p}{p^{2} + 7 p - 18} \cdot \frac{p^{2} - 81}{3 p^{2} - 27 p}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

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In the following exercises, multiply.6p2-6pp2+7p-18·p2-813p2-27p

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Discrete Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply.
$\frac{6 p^{2} - 6 p}{p^{2} + 7 p - 18} \cdot \frac{p^{2} - 81}{3 p^{2} - 27 p}$