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

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

Simplify the denominator.

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

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

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 $b = 3$ .

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

To write $\frac{x}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$\frac{x}{x + 3} \cdot \frac{x - 3}{x - 3} - \frac{6 x}{(x + 3) (x - 3)}$

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $x (x - 3) - 6 x$ .

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

$\frac{x (x - 3) + x \cdot - 6}{(x + 3) (x - 3)}$

Factor $x$ out of $x (x - 3) + x \cdot - 6$ .

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

Subtract $6$ from $- 3$ .

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