Chapter 8: Q 223 (page 954)

Subtract $\frac{- 2 r - 16}{r^{2} + 6 r - 16} - \frac{5}{2 - r}$ .

Short Answer

Expert verified

The difference is $\frac{3}{r - 2}$ .

Step by step solution

Given Information

The Given expression is $\frac{- 2 r - 16}{r^{2} + 6 r - 16} - \frac{5}{2 - r}$ .

Find the LCD of denominators.

Factor the denominators.

$r^{2} + 6 r - 16 = (r - 2) (r + 8)$

LCD $= (r - 2) (r + 8)$

Rewrite the expression in factored form.

$= \frac{- 2 r - 16}{r^{2} + 6 r - 16} - \frac{5}{- (r - 2)} = \frac{- 2 r - 16}{r^{2} + 6 r - 16} + \frac{5}{r - 2}$

$= \frac{- 2 r - 16}{(r - 2) (r + 8)} + \frac{5}{r - 2}$

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{- 2 r - 16}{(r - 2) (r + 8)} + \frac{5 (r + 8)}{(r - 2) (r + 8)}$

Subtract

Take common denominator.

$= \frac{- 2 r - 16 + 5 r + 40}{(r - 2) (r + 8)} = \frac{3 r + 24}{(r - 2) (r + 8)}$

Simplify numerator by cancelling common terms.

$= \frac{3 (r + 8)}{(r - 2) (r + 8)} = \frac{3}{r - 2}$

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Subtract $\frac{- 2 r - 16}{r^{2} + 6 r - 16} - \frac{5}{2 - r}$ .

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Subtract

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Subtract-2r-16r2+6r-16-52-r.

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Subtract

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Geometry

Applied Mathematics

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Logic and Functions

Study anywhere. Anytime. Across all devices.

Subtract $\frac{- 2 r - 16}{r^{2} + 6 r - 16} - \frac{5}{2 - r}$ .