Pre-Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Cancel the common factor of $a b$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

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

Step 4

Cancel the common factor of $a + b$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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