Algebra Examples

$\frac{x^{2} - 16}{x + 6} \div (x + 4)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{x^{2} - 16}{x + 6}}{x + 4}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} - 16}{x + 6} \cdot \frac{1}{x + 4}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{x^{2} - 4^{2}}{x + 6} \cdot \frac{1}{x + 4}$

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 $a = x$ and $b = 4$ .

$\frac{(x + 4) (x - 4)}{x + 6} \cdot \frac{1}{x + 4}$

Step 4

Cancel the common factor of $x + 4$ .

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Step 4.1

Cancel the common factor.

$\frac{(x + 4) (x - 4)}{x + 6} \cdot \frac{1}{x + 4}$

Step 4.2

Rewrite the expression.

$\frac{x - 4}{x + 6}$