simplify, if possible:2x^2-4x/x-2?

(2x² - 4x) / (x - 2)

= 2x(x - 2) / (x - 2) ...... take out the common factor 2x of the numerator

= 2x ...... eliminate (x - 2) in both denominator and numerator, provided that x ≠ 2

It's important to include parentheses.

As written, the division would take precedence, so this would have been equivalent to:
2x² - 4x/x - 2

You could then simplify x/x to 1:
2x² - 4 - 2
2x² - 6
2(x² - 3)

But I'm pretty sure that's NOT what you meant. You probably wanted:
(2x² - 4x) / (x - 2)

Factor out a common 2x from the numerator:
2x(x - 2) / (x - 2)

Now you can cancel the factor of x-2. However, you need to make a note that you originally had a restriction on the domain of x. Previously you couldn't have x - 2 = 0 in the denominator or else you'd be dividing by zero. But once you cancel it, you lose that fact. So be sure to state this at the end.

Answer:
2x, as long as x ≠ 2