Finite Math Examples

$\frac{\frac{a^{2} + b}{a^{2} b - a b^{2}}}{\frac{1}{a - b}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify the denominator.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

Factor $a b$ out of $a b (a) + a b (- 1 b)$ .

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

Step 2.2

Rewrite $- 1 b$ as $- b$ .

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

Step 3

Cancel the common factor of $a - b$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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