Simplify x/(3x-6)*(x-2)/(x+9)

$\frac{x}{3 x - 6} \cdot \frac{x - 2}{x + 9}$

Step 1

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

Factor $3$ out of $3 x$ .

$\frac{x}{3 (x) - 6} \cdot \frac{x - 2}{x + 9}$

Factor $3$ out of $- 6$ .

$\frac{x}{3 x + 3 \cdot - 2} \cdot \frac{x - 2}{x + 9}$

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{x}{3 (x - 2)} \cdot \frac{x - 2}{x + 9}$

Step 2

Cancel the common factor of $x - 2$ .

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

$\frac{x}{(x - 2) \cdot 3} \cdot \frac{x - 2}{x + 9}$

Cancel the common factor.

$\frac{x}{(x - 2) \cdot 3} \cdot \frac{x - 2}{x + 9}$

Rewrite the expression.

$\frac{x}{3} \cdot \frac{1}{x + 9}$

Step 3

Multiply $\frac{x}{3}$ by $\frac{1}{x + 9}$ .

$\frac{x}{3 (x + 9)}$