Simplify (2x+4)/(3x-3)*(12x-12)/(x+5)

$\frac{2 x + 4}{3 x - 3} \cdot \frac{12 x - 12}{x + 5}$

Step 1

Factor $2$ out of $2 x + 4$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $4$ .

$\frac{2 x + 2 \cdot 2}{3 x - 3} \cdot \frac{12 x - 12}{x + 5}$

Factor $2$ out of $2 x + 2 \cdot 2$ .

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

Step 2

Factor $3$ out of $3 x - 3$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 3$ .

$\frac{2 (x + 2)}{3 (x) + 3 (- 1)} \cdot \frac{12 x - 12}{x + 5}$

Factor $3$ out of $3 (x) + 3 (- 1)$ .

$\frac{2 (x + 2)}{3 (x - 1)} \cdot \frac{12 x - 12}{x + 5}$

Step 3

Factor $12$ out of $12 x - 12$ .

Factor $12$ out of $12 x$ .

$\frac{2 (x + 2)}{3 (x - 1)} \cdot \frac{12 (x) - 12}{x + 5}$

Factor $12$ out of $- 12$ .

$\frac{2 (x + 2)}{3 (x - 1)} \cdot \frac{12 (x) + 12 (- 1)}{x + 5}$

Factor $12$ out of $12 (x) + 12 (- 1)$ .

$\frac{2 (x + 2)}{3 (x - 1)} \cdot \frac{12 (x - 1)}{x + 5}$

Step 4

Cancel the common factor of $3 (x - 1)$ .

Factor $3 (x - 1)$ out of $12 (x - 1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Combine $\frac{4}{x + 5}$ and $2$ .

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

Step 6

Multiply $4$ by $2$ .

$\frac{8}{x + 5} (x + 2)$

Step 7

Multiply $\frac{8}{x + 5}$ by $x + 2$ .

$\frac{8 (x + 2)}{x + 5}$