Basic Math Examples

$\frac{a^{2}}{a + 4} \cdot \frac{a^{2} - 16}{3 a}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{a^{2}}{a + 4} \cdot \frac{a^{2} - 4^{2}}{3 a}$

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 $b = 4$ .

$\frac{a^{2}}{a + 4} \cdot \frac{(a + 4) (a - 4)}{3 a}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $a$ .

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Step 2.1.1

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

$\frac{a \cdot a}{a + 4} \cdot \frac{(a + 4) (a - 4)}{3 a}$

Step 2.1.2

Factor $a$ out of $3 a$ .

$\frac{a \cdot a}{a + 4} \cdot \frac{(a + 4) (a - 4)}{a \cdot 3}$

Step 2.1.3

Cancel the common factor.

$\frac{a \cdot a}{a + 4} \cdot \frac{(a + 4) (a - 4)}{a \cdot 3}$

Step 2.1.4

Rewrite the expression.

$\frac{a}{a + 4} \cdot \frac{(a + 4) (a - 4)}{3}$

Step 2.2

Cancel the common factor of $a + 4$ .

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Step 2.2.1

Cancel the common factor.

$\frac{a}{a + 4} \cdot \frac{(a + 4) (a - 4)}{3}$

Step 2.2.2

Rewrite the expression.

$a \cdot \frac{a - 4}{3}$

Step 2.3

Combine $a$ and $\frac{a - 4}{3}$ .

$\frac{a (a - 4)}{3}$