Divide ((x+2)/(x-4))÷(1/(3x-12))

$\frac{x + 2}{x - 4} \div \frac{1}{3 x - 12}$

To divide by a fraction, multiply by its reciprocal.

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

Multiply $\frac{x + 2}{x - 4}$ by $3 x - 12$ .

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

Factor $3$ out of $3 x - 12$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 12$ .

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

Factor $3$ out of $3 x + 3 \cdot - 4$ .

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

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

Cancel the common factor of $x - 4$ .

Cancel the common factor.

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

Divide $(x + 2) \cdot 3$ by $1$ .

$(x + 2) \cdot 3$

Apply the distributive property.

$x \cdot 3 + 2 \cdot 3$

Move $3$ to the left of $x$ .

$3 \cdot x + 2 \cdot 3$

Multiply $2$ by $3$ .

$3 x + 6$