Simplify (2x^2-18x)/(3x+12)*(x+4)/(x-9)

$\frac{2 x^{2} - 18 x}{3 x + 12} \cdot \frac{x + 4}{x - 9}$

Step 1

Factor $2 x$ out of $2 x^{2} - 18 x$ .

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

$\frac{2 x (x) - 18 x}{3 x + 12} \cdot \frac{x + 4}{x - 9}$

Factor $2 x$ out of $- 18 x$ .

$\frac{2 x (x) + 2 x (- 9)}{3 x + 12} \cdot \frac{x + 4}{x - 9}$

Factor $2 x$ out of $2 x (x) + 2 x (- 9)$ .

$\frac{2 x (x - 9)}{3 x + 12} \cdot \frac{x + 4}{x - 9}$

Step 2

Factor $3$ out of $3 x + 12$ .

Factor $3$ out of $3 x$ .

$\frac{2 x (x - 9)}{3 (x) + 12} \cdot \frac{x + 4}{x - 9}$

Factor $3$ out of $12$ .

$\frac{2 x (x - 9)}{3 x + 3 \cdot 4} \cdot \frac{x + 4}{x - 9}$

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

$\frac{2 x (x - 9)}{3 (x + 4)} \cdot \frac{x + 4}{x - 9}$

Step 3

Cancel the common factor of $x - 9$ .

Factor $x - 9$ out of $2 x (x - 9)$ .

$\frac{(x - 9) (2 x)}{3 (x + 4)} \cdot \frac{x + 4}{x - 9}$

Cancel the common factor.

$\frac{(x - 9) (2 x)}{3 (x + 4)} \cdot \frac{x + 4}{x - 9}$

Rewrite the expression.

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

Step 4

Cancel the common factor of $x + 4$ .

Factor $x + 4$ out of $3 (x + 4)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 x}{3}$