Answer
$\displaystyle \frac{4}{x-2}, \qquad x\neq 2$
Work Step by Step
Numerator, factored:$\quad$ $4x-8=4(x-2)$
Denominator, factored:
$x^{2}-4x+4=x^{2}-2\cdot x\cdot 2+2^{2}$=$\quad$... recognize a square of a difference
$=(x-2)^{2}=(x-2)(x-2)$
Numbers to be excluded from the domain are numbers that yield 0 in the denominator:
$x\neq 2$
Expression = $\displaystyle \frac{4(x-2)}{(x-2)(x-2)}$=$\qquad$... cancel $(x-2)$
= $\displaystyle \frac{4}{x-2}, \qquad x\neq 2$
