Simplify ((x-4)/(2x^2))÷((3x-12)/(6x))

$\frac{x - 4}{2 x^{2}} \div \frac{3 x - 12}{6 x}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 4}{2 x^{2}} \cdot \frac{6 x}{3 x - 12}$

Cancel the common factor of $2 x$ .

Factor $2 x$ out of $2 x^{2}$ .

$\frac{x - 4}{2 x (x)} \cdot \frac{6 x}{3 x - 12}$

Factor $2 x$ out of $6 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 4}{x} \cdot \frac{3}{3 x - 12}$

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

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

Cancel the common factor of $3$ and $3 x - 12$ .

Factor $3$ out of $(x - 4) \cdot 3$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 4$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x}$