Which function rule is a rational function x/2 x-2/4 x-2/2 2/x

This expression of yours is problematic in that it's difficult to know which math operations are intended and in which order.   In   x/2 x-2/4 x-2/2 , which part of the expression is in the numerator, and which in the denominator?

x shows up 3 times.  Apparently you meant "the variable x" in "x/2."  What about the next "x?" Did you type that in to indicate multiplication or is that "x" a variable also?  I think you catch my drift:  Your post will need some editing before your readers can understand what you want to do here.

Suppose I interpret your   x/2 x-2/4 x-2/2  to mean the following:

( x/2 )
* (x-2/2).  If that wasn't your intent, please fix it.
 x - 2/4

If this interpretation is correct, then you have

      x(x-1)          2x(x-1)
= .  If not, please fix it.  This rational function
     x-1/2            2x -1        cannot be reduced.