Algebra Examples

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

Step 1

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 $b = b$ .

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $a - b$ .

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Step 2.1.1

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

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

Cancel the common factor of $a$ .

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Cancel the common factor.

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

Step 2.2.4

Rewrite the expression.

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

Step 2.3

Combine $\frac{a + b}{2 b}$ and $a$ .

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

Step 2.4

Reorder factors in $\frac{(a + b) a}{2 b}$ .

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