Algebra Examples

$\frac{- 6}{x + 6} - \frac{4}{x - 6}$

Step 1

Move the negative in front of the fraction.

$- \frac{6}{x + 6} - \frac{4}{x - 6}$

Step 2

To write $- \frac{6}{x + 6}$ as a fraction with a common denominator, multiply by $\frac{x - 6}{x - 6}$ .

$- \frac{6}{x + 6} \cdot \frac{x - 6}{x - 6} - \frac{4}{x - 6}$

Step 3

To write $- \frac{4}{x - 6}$ as a fraction with a common denominator, multiply by $\frac{x + 6}{x + 6}$ .

$- \frac{6}{x + 6} \cdot \frac{x - 6}{x - 6} - \frac{4}{x - 6} \cdot \frac{x + 6}{x + 6}$

Step 4

Write each expression with a common denominator of $(x + 6) (x - 6)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{6}{x + 6}$ by $\frac{x - 6}{x - 6}$ .

$- \frac{6 (x - 6)}{(x + 6) (x - 6)} - \frac{4}{x - 6} \cdot \frac{x + 6}{x + 6}$

Step 4.2

Multiply $\frac{4}{x - 6}$ by $\frac{x + 6}{x + 6}$ .

$- \frac{6 (x - 6)}{(x + 6) (x - 6)} - \frac{4 (x + 6)}{(x - 6) (x + 6)}$

Step 4.3

Reorder the factors of $(x - 6) (x + 6)$ .

$- \frac{6 (x - 6)}{(x + 6) (x - 6)} - \frac{4 (x + 6)}{(x + 6) (x - 6)}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 6 (x - 6) - 4 (x + 6)}{(x + 6) (x - 6)}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $- 2$ out of $- 6 (x - 6) - 4 (x + 6)$ .

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Step 6.1.1

Factor $- 2$ out of $- 6 (x - 6)$ .

$\frac{- 2 (3 (x - 6)) - 4 (x + 6)}{(x + 6) (x - 6)}$

Step 6.1.2

Factor $- 2$ out of $- 4 (x + 6)$ .

$\frac{- 2 (3 (x - 6)) - 2 (2 (x + 6))}{(x + 6) (x - 6)}$

Step 6.1.3

Factor $- 2$ out of $- 2 (3 (x - 6)) - 2 (2 (x + 6))$ .

$\frac{- 2 (3 (x - 6) + 2 (x + 6))}{(x + 6) (x - 6)}$

Step 6.2

Apply the distributive property.

$\frac{- 2 (3 x + 3 \cdot - 6 + 2 (x + 6))}{(x + 6) (x - 6)}$

Step 6.3

Multiply $3$ by $- 6$ .

$\frac{- 2 (3 x - 18 + 2 (x + 6))}{(x + 6) (x - 6)}$

Step 6.4

Apply the distributive property.

$\frac{- 2 (3 x - 18 + 2 x + 2 \cdot 6)}{(x + 6) (x - 6)}$

Step 6.5

Multiply $2$ by $6$ .

$\frac{- 2 (3 x - 18 + 2 x + 12)}{(x + 6) (x - 6)}$

Step 6.6

Add $3 x$ and $2 x$ .

$\frac{- 2 (5 x - 18 + 12)}{(x + 6) (x - 6)}$

Step 6.7

Add $- 18$ and $12$ .

$\frac{- 2 (5 x - 6)}{(x + 6) (x - 6)}$

Step 7

Move the negative in front of the fraction.

$- \frac{2 (5 x - 6)}{(x + 6) (x - 6)}$