Basic Math Examples

$\frac{m^{2} - 16}{5 m} \div (m + 4)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{m^{2} - 16}{5 m}}{m + 4}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{m^{2} - 16}{5 m} \cdot \frac{1}{m + 4}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{m^{2} - 4^{2}}{5 m} \cdot \frac{1}{m + 4}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = 4$ .

$\frac{(m + 4) (m - 4)}{5 m} \cdot \frac{1}{m + 4}$

Step 4

Cancel the common factor of $m + 4$ .

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Step 4.1

Cancel the common factor.

$\frac{(m + 4) (m - 4)}{5 m} \cdot \frac{1}{m + 4}$

Step 4.2

Rewrite the expression.

$\frac{m - 4}{5 m}$