Simplify (x/(3x-9))/((x+2)/(x^2-9))

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

Multiply the numerator by the reciprocal of the denominator.

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

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

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 9$ .

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

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

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

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

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

Simplify terms.

Cancel the common factor of $x - 3$ .

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{x}{3}$ by $\frac{x + 3}{x + 2}$ .

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