Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $2 a b$ .

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Step 2.1.1

Factor $2 a b$ out of $4 a b$ .

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

Multiply $\frac{1}{a^{2} - b^{2}}$ by $\frac{{(a - b)}^{2}}{2}$ .

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

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 $b = b$ .

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of ${(a - b)}^{2}$ and $a - b$ .

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Step 4.1.1

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

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

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

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

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

Step 4.1.2.2

Cancel the common factor.

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

Step 4.1.2.3

Rewrite the expression.

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

Step 4.2

Move $2$ to the left of $a + b$ .

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