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

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

Step 1

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

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

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

Factor $3 x$ out of $- 6 x$ .

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

Factor $3 x$ out of $3 x (x) + 3 x (- 2)$ .

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

Step 2

Cancel the common factor of $x - 2$ .

Factor $x - 2$ out of $3 x (x - 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{12 x^{2}} \cdot \frac{4}{3 x}$

Step 3

Cancel the common factor of $4$ .

Factor $4$ out of $12 x^{2}$ .

$\frac{1}{4 (3 x^{2})} \cdot \frac{4}{3 x}$

Cancel the common factor.

$\frac{1}{4 (3 x^{2})} \cdot \frac{4}{3 x}$

Rewrite the expression.

$\frac{1}{3 x^{2}} \cdot \frac{1}{3 x}$

Step 4

Multiply $\frac{1}{3 x^{2}}$ by $\frac{1}{3 x}$ .

$\frac{1}{3 x^{2} (3 x)}$

Step 5

Multiply $3$ by $3$ .

$\frac{1}{9 x^{2} x}$

Step 6

Raise $x$ to the power of $1$ .

$\frac{1}{9 (x^{1} x^{2})}$

Step 7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{9 x^{1 + 2}}$

Step 8

Add $1$ and $2$ .

$\frac{1}{9 x^{3}}$