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

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

Cancel the common factor of $3 x - 12$ and $6$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 12$ .

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

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

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

Cancel the common factors.

Factor $3$ out of $6 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{\frac{x - 4}{2 x^{2}}}{\frac{x - 4}{2 x}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{x - 4}{2 x^{2}} \cdot \frac{2 x}{x - 4}$

Cancel the common factor of $x - 4$ .

Cancel the common factor.

$\frac{x - 4}{2 x^{2}} \cdot \frac{2 x}{x - 4}$

Rewrite the expression.

$\frac{1}{2 x^{2}} (2 x)$

Cancel the common factor of $2 x$ .

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

$\frac{1}{2 x (x)} (2 x)$

Cancel the common factor.

$\frac{1}{2 x \cdot x} (2 x)$

Rewrite the expression.

$\frac{1}{x}$