Simplify (a^3b^6)/(a^2b^3-a^4b^2)

$\frac{a^{3} b^{6}}{a^{2} b^{3} - a^{4} b^{2}}$

Step 1

Factor $a^{2} b^{2}$ out of $a^{2} b^{3} - a^{4} b^{2}$ .

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

$\frac{a^{3} b^{6}}{a^{2} b^{2} (b) - a^{4} b^{2}}$

Factor $a^{2} b^{2}$ out of $- a^{4} b^{2}$ .

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

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

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

Step 2

Cancel the common factor of $a^{3}$ and $a^{2}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $b^{6}$ and $b^{2}$ .

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

$\frac{b^{2} (a b^{4})}{b^{2} (b - a^{2})}$

Cancel the common factors.

Cancel the common factor.

$\frac{b^{2} (a b^{4})}{b^{2} (b - a^{2})}$

Rewrite the expression.

$\frac{a b^{4}}{b - a^{2}}$