#### Answer

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

#### Work Step by Step

To simplify, divide both the numerator and denominator by their greatest common factor.
Use the the factorization to find the GCF.
$\frac{4x-8}{x^2-4x+4}=\frac{4(x-2)}{(x-2)(x-2)}=\frac{4(x-2)\div(x-2)}{(x-2)(x-2)\div(x-2)}=\frac{4}{x-2}$