Divide (x^2-8x+16)/(2x-8)

$\frac{x^{2} - 8 x + 16}{2 x - 8}$

Step 1

Factor using the perfect square rule.

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

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

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 x = 2 \cdot x \cdot 4$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 4$ .

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

Step 2

Factor $2$ out of $2 x - 8$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 8$ .

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

Factor $2$ out of $2 x + 2 \cdot - 4$ .

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

Step 3

Cancel the common factor of ${(x - 4)}^{2}$ and $x - 4$ .

Factor $x - 4$ out of ${(x - 4)}^{2}$ .

$\frac{(x - 4) (x - 4)}{2 (x - 4)}$

Cancel the common factors.

Factor $x - 4$ out of $2 (x - 4)$ .

$\frac{(x - 4) (x - 4)}{(x - 4) \cdot 2}$

Cancel the common factor.

$\frac{(x - 4) (x - 4)}{(x - 4) \cdot 2}$

Rewrite the expression.

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

Step 4

Split the fraction $\frac{x - 4}{2}$ into two fractions.

$\frac{x}{2} + \frac{- 4}{2}$

Step 5

Divide $- 4$ by $2$ .

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