Division where one denominator is x-2 and second is 2. Test on monday!

I can solve something like $\displaystyle (y-3/y)=(10y^2/y^2)$ where I can get the Lowest Common Denominator $\displaystyle y^2$.

What I don't get is how to solve these kinds of problems, where I can't find the Lowest Common Denominator (or at least I don't know how):

$\displaystyle (2/x-2)-(x/2)=(x/x-2)$

I tried getting the LCD by doing like this but I don't get the correct answer:

LCD:

$\displaystyle (x-2): 1*(x-2)

2: 1*2

LCD: 1*2*(x-2) = 2x-4$

Appreciate Answers ;)