Simplify (m^2-9)/(3m^3-3m^2)

$\frac{m^{2} - 9}{3 m^{3} - 3 m^{2}}$

Simplify the numerator.

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

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

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

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

Factor $3 m^{2}$ out of $3 m^{3} - 3 m^{2}$ .

Factor $3 m^{2}$ out of $3 m^{3}$ .

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

Factor $3 m^{2}$ out of $- 3 m^{2}$ .

$\frac{(m + 3) (m - 3)}{3 m^{2} (m) + 3 m^{2} (- 1)}$

Factor $3 m^{2}$ out of $3 m^{2} (m) + 3 m^{2} (- 1)$ .

$\frac{(m + 3) (m - 3)}{3 m^{2} (m - 1)}$