Simplify (3a^2b-6ab+5ab^2)(ab)^-1

$(3 a^{2} b - 6 a b + 5 a b^{2}) {(a b)}^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(3 a^{2} b - 6 a b + 5 a b^{2}) \frac{1}{a b}$

Multiply $3 a^{2} b - 6 a b + 5 a b^{2}$ by $\frac{1}{a b}$ .

$\frac{3 a^{2} b - 6 a b + 5 a b^{2}}{a b}$

Factor $a b$ out of $3 a^{2} b - 6 a b + 5 a b^{2}$ .

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

$\frac{a b (3 a) - 6 a b + 5 a b^{2}}{a b}$

Factor $a b$ out of $- 6 a b$ .

$\frac{a b (3 a) + a b (- 6) + 5 a b^{2}}{a b}$

Factor $a b$ out of $5 a b^{2}$ .

$\frac{a b (3 a) + a b (- 6) + a b (5 b)}{a b}$

Factor $a b$ out of $a b (3 a) + a b (- 6)$ .

$\frac{a b (3 a - 6) + a b (5 b)}{a b}$

Factor $a b$ out of $a b (3 a - 6) + a b (5 b)$ .

$\frac{a b (3 a - 6 + 5 b)}{a b}$

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a b (3 a - 6 + 5 b)}{a b}$

Rewrite the expression.

$\frac{b (3 a - 6 + 5 b)}{b}$

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{b (3 a - 6 + 5 b)}{b}$

Divide $3 a - 6 + 5 b$ by $1$ .

$3 a - 6 + 5 b$

Move $- 6$ .

$3 a + 5 b - 6$