Simplify (6a^3b^2)/(3a^2b-6ab^2)

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

Step 1

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

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

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

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

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

Factor $3 a b$ out of $3 a b (a) + 3 a b (- 2 b)$ .

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

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

Step 2

Cancel the common factor of $6$ and $3$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 3

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

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

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

Cancel the common factors.

Factor $a$ out of $a b (a - 2 b)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 4

Cancel the common factor of $b^{2}$ and $b$ .

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

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 a^{2} b}{a - 2 b}$

$\frac{2 a^{2} b}{a - 2 b}$

$\frac{2 a^{2} b}{a - 2 b}$

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