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

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

Step 1

Factor $3$ out of $3 x - 9$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 9$ .

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

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

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

Step 2

Cancel the common factor of $x$ .

Factor $x$ out of $4 x$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x - 3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$4 \cdot \frac{3}{x}$

Step 4

Combine $4$ and $\frac{3}{x}$ .

$\frac{4 \cdot 3}{x}$

Step 5

Multiply $4$ by $3$ .

$\frac{12}{x}$