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

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

Simplify each term.

Factor $2$ out of $2 x - 6$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 6$ .

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

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

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

Simplify the denominator.

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

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

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 $b = 3$ .

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

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Combine the numerators over the common denominator.

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