Simplify (4x)/(4x^2+9)*(6x-9)/(12x)

$\frac{4 x}{4 x^{2} + 9} \cdot \frac{6 x - 9}{12 x}$

Factor $3$ out of $6 x - 9$ .

Factor $3$ out of $6 x$ .

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

Factor $3$ out of $- 9$ .

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

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

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

Cancel the common factor of $4 x$ .

Factor $4 x$ out of $12 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{4 x^{2} + 9} \cdot \frac{3 (2 x - 3)}{3}$

Multiply $\frac{1}{4 x^{2} + 9}$ by $\frac{3 (2 x - 3)}{3}$ .

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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