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

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

Simplify the denominator.

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

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

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 $b = 3$ .

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

Factor $x$ out of $6 x$ .

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

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

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

Subtract $3$ from $6$ .

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

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

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