Chapter 7: Q. 127 (page 668)

In the following exercises, perform indicated operations.
$\frac{- 9 p - 17}{p^{2} - 4 p - 21} - \frac{p + 1}{7 - p}$

Short Answer

Expert verified

The resultant expression is $\frac{p + 2}{p + 3}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{- 9 p - 17}{p^{2} - 4 p - 21} - \frac{p + 1}{7 - p}$ .

Step 2. Express with LCD

The LCD of the given expressions to subtract is $(p - 7) (p + 3)$ .
Express the given expression with LCD.

$\begin{array}{rcl} \frac{- 9 p - 17}{p^{2} - 4 p - 21} - \frac{p + 1}{7 - p} & = & \frac{- 9 p - 17}{(p - 7) (p + 3)} - \frac{- (p + 1) (p + 3)}{(p - 7) (p + 3)} \\ = & \frac{- 9 p - 17}{(p - 7) (p + 3)} - \frac{- p^{2} - 4 p - 3}{(p - 7) (p + 3)} \end{array}$

Step 3. Simplify

As the denominator is the same for both the terms, perform addition in the numerator and place it over the common denominator.

$\frac{- 9 p - 17 + p^{2} + 4 p + 3}{(p - 7) (p + 3)} = \frac{p^{2} - 5 p + 14}{(p - 7) (p + 3)}$

Cancel out the common factor from numerator and denominator.

$\frac{(p - 7) (p + 2)}{(p - 7) (p + 3)} = \frac{p + 2}{p + 3}$

So, the resultant expression is $\frac{p + 2}{p + 3}$ .

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In the following exercises, perform indicated operations.
$\frac{- 9 p - 17}{p^{2} - 4 p - 21} - \frac{p + 1}{7 - p}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with LCD

Step 3. Simplify

One App. One Place for Learning.

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In the following exercises, perform indicated operations. -9p-17p2-4p-21-p+17-p

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with LCD

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Calculus

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.
$\frac{- 9 p - 17}{p^{2} - 4 p - 21} - \frac{p + 1}{7 - p}$