Simplify (2x^2-8x+8)/(x^2-4)

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

Simplify the numerator.

Factor $2$ out of $2 x^{2} - 8 x + 8$ .

Factor $2$ out of $2 x^{2}$ .

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

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

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

Factor $2$ out of $8$ .

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

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

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

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

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

Factor using the perfect square rule.

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

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

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

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

Rewrite the polynomial.

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

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

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

Simplify the denominator.

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

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

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 $b = 2$ .

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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