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

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

Cancel the common factor of $6$ and $2 y - 6$ .

Factor $2$ out of $6$ .

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

Cancel the common factors.

Factor $2$ out of $2 y$ .

$\frac{y^{2}}{y - 3} - \frac{2 \cdot 3}{2 (y) - 6}$

Factor $2$ out of $- 6$ .

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

Factor $2$ out of $2 (y) + 2 (- 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine the numerators over the common denominator.

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