Simplify ((x^2-16)/(x+6))÷(x+4)

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

Rewrite the division as a fraction.

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

Multiply the numerator by the reciprocal of the denominator.

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

Simplify the numerator.

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

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

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 $b = 4$ .

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

Cancel the common factor of $x + 4$ .

Cancel the common factor.

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

Rewrite the expression.

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