Pre-Algebra Examples

$\frac{- 5}{x - 3} - \frac{- 4}{x + 2}$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

$- \frac{5}{x - 3} - \frac{- 4}{x + 2}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{5}{x - 3} - - \frac{4}{x + 2}$

Step 1.3

Multiply $- - \frac{4}{x + 2}$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$- \frac{5}{x - 3} + 1 \frac{4}{x + 2}$

Step 1.3.2

Multiply $\frac{4}{x + 2}$ by $1$ .

$- \frac{5}{x - 3} + \frac{4}{x + 2}$

Step 2

To write $- \frac{5}{x - 3}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$- \frac{5}{x - 3} \cdot \frac{x + 2}{x + 2} + \frac{4}{x + 2}$

Step 3

To write $\frac{4}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$- \frac{5}{x - 3} \cdot \frac{x + 2}{x + 2} + \frac{4}{x + 2} \cdot \frac{x - 3}{x - 3}$

Step 4

Write each expression with a common denominator of $(x - 3) (x + 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{x - 3}$ by $\frac{x + 2}{x + 2}$ .

$- \frac{5 (x + 2)}{(x - 3) (x + 2)} + \frac{4}{x + 2} \cdot \frac{x - 3}{x - 3}$

Step 4.2

Multiply $\frac{4}{x + 2}$ by $\frac{x - 3}{x - 3}$ .

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

Step 4.3

Reorder the factors of $(x - 3) (x + 2)$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{- 5 x - 5 \cdot 2 + 4 (x - 3)}{(x + 2) (x - 3)}$

Step 6.2

Multiply $- 5$ by $2$ .

$\frac{- 5 x - 10 + 4 (x - 3)}{(x + 2) (x - 3)}$

Step 6.3

Apply the distributive property.

$\frac{- 5 x - 10 + 4 x + 4 \cdot - 3}{(x + 2) (x - 3)}$

Step 6.4

Multiply $4$ by $- 3$ .

$\frac{- 5 x - 10 + 4 x - 12}{(x + 2) (x - 3)}$

Step 6.5

Add $- 5 x$ and $4 x$ .

$\frac{- x - 10 - 12}{(x + 2) (x - 3)}$

Step 6.6

Subtract $12$ from $- 10$ .

$\frac{- x - 22}{(x + 2) (x - 3)}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- x$ .

$\frac{- (x) - 22}{(x + 2) (x - 3)}$

Step 7.2

Rewrite $- 22$ as $- 1 (22)$ .

$\frac{- (x) - 1 (22)}{(x + 2) (x - 3)}$

Step 7.3

Factor $- 1$ out of $- (x) - 1 (22)$ .

$\frac{- (x + 22)}{(x + 2) (x - 3)}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (x + 22)$ as $- 1 (x + 22)$ .

$\frac{- 1 (x + 22)}{(x + 2) (x - 3)}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{x + 22}{(x + 2) (x - 3)}$