Simplify ((3x)/(2x-4))÷((6x^2)/(x-2))

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify terms.

Cancel the common factor of $3 x$ .

Factor $3 x$ out of $6 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2 x - 4} \cdot \frac{x - 2}{2 x}$

Multiply $\frac{1}{2 x - 4}$ by $\frac{x - 2}{2 x}$ .

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

Step 3

Simplify the denominator.

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 4$ .

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

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

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

Multiply $2$ by $2$ .

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

Step 4

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{4 x}$