The rational expression is:

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

Step 1: Factor the numerator

The numerator $4x - 8$ has a common factor of 4:

$4x - 8 = 4(x - 2)$

Step 2: Factor the denominator

The denominator $x^2 - 4x + 4$ is a perfect square trinomial:

$x^2 - 4x + 4 = (x - 2)^2$

Step 3: Simplify the expression

Now, the rational expression becomes:

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

You can cancel out one factor of $x - 2$ from the numerator and denominator (assuming $x \neq 2$ to avoid division by zero):

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

So, the simplified expression is:

$\frac{4}{x - 2} \quad \text{(for } x \neq 2\text{)}$

Would you like further details or have any questions?

Here are some related questions:

1. What is a perfect square trinomial, and how do you recognize it?
2. How do you factor more complex trinomials?
3. How do you handle rational expressions when there's no common factor?
4. What happens if $x = 2$ in this expression?
5. How do you simplify complex rational expressions involving multiple terms?

Tip: Always check for common factors in both the numerator and denominator before simplifying a rational expression.