Chapter 7: Q. 418 (page 736)

In the following exercises, perform the indicated operations .
$\frac{- 3 w - 15}{w^{2} + w - 20} - \frac{w + 2}{4 - w}$

Short Answer

Expert verified

Simplified expression is $\frac{w - 1}{w - 4}$

Step by step solution

Step 1. Given Information

Expression :

\frac{- 3 w - 15}{w^{2} + w - 20} - \frac{w + 2}{4 - w}

it can be rewritten as

$\frac{- (3 w + 15)}{w^{2} + w - 20} - \frac{w + 2}{- (w - 4)} = \frac{- (3 w + 15)}{w^{2} + w - 20} + \frac{w + 2}{w - 4}$

Step 2. Find LCD

Denominator of first fraction is $w^{2} + w - 20$

factorize this denominator

$w^{2} + 5 w - 4 w - 20 = w (w + 5) - 4 (w + 5) = (w + 5) (w - 4)$

Denominator of the second fraction

It can be written as $((w - 4))$

here $(w - 4)$ is common between both denominator

So the LCD is $(w + 5) (w - 4)$

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

$\frac{- (3 w + 15)}{(w + 5) (w - 4)} + \frac{(w + 2) (w + 5)}{(w + 5) (w - 4)}$

Step 4.Simplify the numerators.

$\frac{- 3 w - 15}{(w + 5) (w - 4)} + \frac{(w^{2} + 5 w + 2 w + 10)}{(w + 5) (w - 4)} = \frac{- 3 w - 15}{(w + 5) (w - 4)} + \frac{w^{2} + 7 w + 10}{(w + 5) (w - 4)}$

Step 5. Add numerators

$\frac{- 3 w - 15 + w^{2} + 7 w + 10}{(w + 5) (w - 4)}$

Step 6. Simplify numerator

$\frac{w^{2} + 4 w - 5}{(w + 5) (w - 4)}$

Step 7. Factorize numerator and remove common factor

$\frac{w^{2} + 5 w - w - 5}{(w + 5) (w - 4)} = \frac{w (w + 5) - 1 (w + 5)}{(w + 5) (w - 4)} = \frac{(w + 5) (w - 1)}{(w + 5) (w - 4)} = \frac{w - 1}{w - 4}$

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In the following exercises, perform the indicated operations .
$\frac{- 3 w - 15}{w^{2} + w - 20} - \frac{w + 2}{4 - w}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find LCD

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

Step 4.Simplify the numerators.

Step 5. Add numerators

Step 6. Simplify numerator

Step 7. Factorize numerator and remove common factor

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In the following exercises, perform the indicated operations .-3w-15w2+w-20-w+24-w

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find LCD

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

Step 4.Simplify the numerators.

Step 5. Add numerators

Step 6. Simplify numerator

Step 7. Factorize numerator and remove common factor

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Statistics

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, perform the indicated operations .
$\frac{- 3 w - 15}{w^{2} + w - 20} - \frac{w + 2}{4 - w}$