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

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

Simplify the denominator.

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

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

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

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

Factor $y$ out of $- 6 y$ .

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

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

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

Subtract $6$ from $- 3$ .

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