Basic Math Examples

$\frac{a}{a^{2} - 16} \cdot \frac{a + 4}{a - 2}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $16$ as $4^{2}$ .

$\frac{a}{a^{2} - 4^{2}} \cdot \frac{a + 4}{a - 2}$

Step 1.2

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 $b = 4$ .

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $a + 4$ .

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Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Rewrite the expression.

$\frac{a}{a - 4} \cdot \frac{1}{a - 2}$

Step 2.2

Multiply $\frac{a}{a - 4}$ by $\frac{1}{a - 2}$ .

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