Chapter 8: Q 221 (page 954)

Subtract $\frac{- 9 p - 17}{p^{2} - 4 p - 21} - \frac{p + 1}{7 - p}$ .

Short Answer

Expert verified

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

Step by step solution

Given Information

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

Find the LCD of denominators.

Factor the denominators.

$p^{2} - 4 p - 21 = (p - 7) (p + 3)$

$7 - p = - (p - 7)$

LCD $= (p - 7) (p + 3)$

Rewrite the expression in factored form.

$= \frac{- 9 p - 17}{(p - 7) (p + 3)} - \frac{- p - 1}{(p - 7)}$

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{- 9 p - 17}{(p - 7) (p + 3)} - \frac{(- p - 1) (p + 3)}{(p - 7) (p + 3)}$

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

Subtract and simplify the numerator.

Take common denominator.

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

Simplify numerator.

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

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

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

Cancel out common factors.

$= \frac{p + 2}{p + 3}$

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Subtract $\frac{- 9 p - 17}{p^{2} - 4 p - 21} - \frac{p + 1}{7 - p}$ .

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Subtract and simplify the numerator.

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Subtract-9p-17p2-4p-21-p+17-p.

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Subtract and simplify the numerator.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Geometry

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Subtract $\frac{- 9 p - 17}{p^{2} - 4 p - 21} - \frac{p + 1}{7 - p}$ .