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

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

Factor $4$ out of $4 x - 8$ .

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Factor $4$ out of $4 x$ .

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

Factor $4$ out of $- 8$ .

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

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

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

Factor using the perfect square rule.

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

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

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot x \cdot - 2$

Simplify.

$2 a b = - 4 x$

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

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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