Divide ((x^2-4)/(x-8))÷(x-2)

$\frac{x^{2} - 4}{x - 8} \div (x - 2)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{x^{2} - 4}{x - 8}}{x - 2}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} - 4}{x - 8} \cdot \frac{1}{x - 2}$

Step 3

Simplify the numerator.

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

$\frac{x^{2} - 2^{2}}{x - 8} \cdot \frac{1}{x - 2}$

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 $b = 2$ .

$\frac{(x + 2) (x - 2)}{x - 8} \cdot \frac{1}{x - 2}$

Step 4

Cancel the common factor of $x - 2$ .

Factor $x - 2$ out of $(x + 2) (x - 2)$ .

$\frac{(x - 2) (x + 2)}{x - 8} \cdot \frac{1}{x - 2}$

Cancel the common factor.

$\frac{(x - 2) (x + 2)}{x - 8} \cdot \frac{1}{x - 2}$

Rewrite the expression.

$\frac{x + 2}{x - 8}$