Divide ((6x+6)/7)÷((4x+4)/(x-2))

$\frac{6 x + 6}{7} \div \frac{4 x + 4}{x - 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 x + 6}{7} \cdot \frac{x - 2}{4 x + 4}$

Step 2

Factor $6$ out of $6 x + 6$ .

Factor $6$ out of $6 x$ .

$\frac{6 (x) + 6}{7} \cdot \frac{x - 2}{4 x + 4}$

Factor $6$ out of $6$ .

$\frac{6 (x) + 6 (1)}{7} \cdot \frac{x - 2}{4 x + 4}$

Factor $6$ out of $6 (x) + 6 (1)$ .

$\frac{6 (x + 1)}{7} \cdot \frac{x - 2}{4 x + 4}$

Step 3

Factor $4$ out of $4 x + 4$ .

Factor $4$ out of $4 x$ .

$\frac{6 (x + 1)}{7} \cdot \frac{x - 2}{4 (x) + 4}$

Factor $4$ out of $4$ .

$\frac{6 (x + 1)}{7} \cdot \frac{x - 2}{4 (x) + 4 (1)}$

Factor $4$ out of $4 (x) + 4 (1)$ .

$\frac{6 (x + 1)}{7} \cdot \frac{x - 2}{4 (x + 1)}$

Step 4

Cancel the common factor of $2 (x + 1)$ .

Factor $2 (x + 1)$ out of $6 (x + 1)$ .

$\frac{2 (x + 1) (3)}{7} \cdot \frac{x - 2}{4 (x + 1)}$

Factor $2 (x + 1)$ out of $4 (x + 1)$ .

$\frac{2 (x + 1) (3)}{7} \cdot \frac{x - 2}{2 (x + 1) (2)}$

Cancel the common factor.

$\frac{2 (x + 1) \cdot 3}{7} \cdot \frac{x - 2}{2 (x + 1) \cdot 2}$

Rewrite the expression.

$\frac{3}{7} \cdot \frac{x - 2}{2}$

Step 5

Multiply $\frac{3}{7}$ by $\frac{x - 2}{2}$ .

$\frac{3 (x - 2)}{7 \cdot 2}$

Step 6

Multiply $7$ by $2$ .

$\frac{3 (x - 2)}{14}$

Step 7

Apply the distributive property.

$\frac{3 x + 3 \cdot - 2}{14}$

Step 8

Multiply $3$ by $- 2$ .

$\frac{3 x - 6}{14}$

Step 9

Split the fraction $\frac{3 x - 6}{14}$ into two fractions.

$\frac{3 x}{14} + \frac{- 6}{14}$

Step 10

Cancel the common factor of $- 6$ and $14$ .

Factor $2$ out of $- 6$ .

$\frac{3 x}{14} + \frac{2 (- 3)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$\frac{3 x}{14} + \frac{2 \cdot - 3}{2 \cdot 7}$

Cancel the common factor.

$\frac{3 x}{14} + \frac{2 \cdot - 3}{2 \cdot 7}$

Rewrite the expression.

$\frac{3 x}{14} + \frac{- 3}{7}$

Step 11

Move the negative in front of the fraction.

$\frac{3 x}{14} - \frac{3}{7}$

Divide ((6x+6)/7)÷((4x+4)/(x-2))

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