Simplify (a^2b(b-3))/(b^3(b-3)^2)

$\frac{a^{2} b (b - 3)}{b^{3} {(b - 3)}^{2}}$

Cancel the common factor of $b$ and $b^{3}$ .

Factor $b$ out of $a^{2} b (b - 3)$ .

$\frac{b (a^{2} (b - 3))}{b^{3} {(b - 3)}^{2}}$

Cancel the common factors.

Factor $b$ out of $b^{3} {(b - 3)}^{2}$ .

$\frac{b (a^{2} (b - 3))}{b (b^{2} {(b - 3)}^{2})}$

Cancel the common factor.

$\frac{b (a^{2} (b - 3))}{b (b^{2} {(b - 3)}^{2})}$

Rewrite the expression.

$\frac{a^{2} (b - 3)}{b^{2} {(b - 3)}^{2}}$

Cancel the common factor of $b - 3$ and ${(b - 3)}^{2}$ .

Factor $b - 3$ out of $a^{2} (b - 3)$ .

$\frac{(b - 3) a^{2}}{b^{2} {(b - 3)}^{2}}$

Cancel the common factors.

Factor $b - 3$ out of $b^{2} {(b - 3)}^{2}$ .

$\frac{(b - 3) a^{2}}{(b - 3) (b^{2} (b - 3))}$

Cancel the common factor.

$\frac{(b - 3) a^{2}}{(b - 3) (b^{2} (b - 3))}$

Rewrite the expression.

$\frac{a^{2}}{b^{2} (b - 3)}$