Examples

$\frac{2}{x + 7} - \frac{4}{x + 9}$

Step 1

To write $\frac{2}{x + 7}$ as a fraction with a common denominator, multiply by $\frac{x + 9}{x + 9}$ .

$\frac{2}{x + 7} \cdot \frac{x + 9}{x + 9} - \frac{4}{x + 9}$

Step 2

To write $- \frac{4}{x + 9}$ as a fraction with a common denominator, multiply by $\frac{x + 7}{x + 7}$ .

$\frac{2}{x + 7} \cdot \frac{x + 9}{x + 9} - \frac{4}{x + 9} \cdot \frac{x + 7}{x + 7}$

Step 3

Write each expression with a common denominator of $(x + 7) (x + 9)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2}{x + 7}$ by $\frac{x + 9}{x + 9}$ .

$\frac{2 (x + 9)}{(x + 7) (x + 9)} - \frac{4}{x + 9} \cdot \frac{x + 7}{x + 7}$

Step 3.2

Multiply $\frac{4}{x + 9}$ by $\frac{x + 7}{x + 7}$ .

$\frac{2 (x + 9)}{(x + 7) (x + 9)} - \frac{4 (x + 7)}{(x + 9) (x + 7)}$

Step 3.3

Reorder the factors of $(x + 9) (x + 7)$ .

$\frac{2 (x + 9)}{(x + 7) (x + 9)} - \frac{4 (x + 7)}{(x + 7) (x + 9)}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 (x + 9) - 4 (x + 7)}{(x + 7) (x + 9)}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $2$ out of $2 (x + 9) - 4 (x + 7)$ .

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Step 5.1.1

Factor $2$ out of $- 4 (x + 7)$ .

$\frac{2 (x + 9) + 2 (- 2 (x + 7))}{(x + 7) (x + 9)}$

Step 5.1.2

Factor $2$ out of $2 (x + 9) + 2 (- 2 (x + 7))$ .

$\frac{2 (x + 9 - 2 (x + 7))}{(x + 7) (x + 9)}$

Step 5.2

Apply the distributive property.

$\frac{2 (x + 9 - 2 x - 2 \cdot 7)}{(x + 7) (x + 9)}$

Step 5.3

Multiply $- 2$ by $7$ .

$\frac{2 (x + 9 - 2 x - 14)}{(x + 7) (x + 9)}$

Step 5.4

Subtract $2 x$ from $x$ .

$\frac{2 (- x + 9 - 14)}{(x + 7) (x + 9)}$

Step 5.5

Subtract $14$ from $9$ .

$\frac{2 (- x - 5)}{(x + 7) (x + 9)}$

Step 6

Simplify with factoring out.

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Step 6.1

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

$\frac{2 (- (x) - 5)}{(x + 7) (x + 9)}$

Step 6.2

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{2 (- (x) - 1 (5))}{(x + 7) (x + 9)}$

Step 6.3

Factor $- 1$ out of $- (x) - 1 (5)$ .

$\frac{2 (- (x + 5))}{(x + 7) (x + 9)}$

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite $- (x + 5)$ as $- 1 (x + 5)$ .

$\frac{2 (- 1 (x + 5))}{(x + 7) (x + 9)}$

Step 6.4.2

Move the negative in front of the fraction.

$- \frac{2 (x + 5)}{(x + 7) (x + 9)}$

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