Simplification of polynomial division

[MeDiCS]

1. The problem statement, all variables and given/known data
For all x>2, \frac{2x²+2x-12}{x-2} simplifies to:
2(x - 2), x + 3, 2(x + 3)(x - 2), x - 2 or 2(x + 3).
(Problem taken from http://www.analyzemath.com/practice_tests/act/act_sample_1.html, question five).


2. Relevant equations
None, AFAIK.


3. The attempt at a solution
I have seen the answer (which is 2(x+3)), but I couldn't figure out how to get there.

[Mark44]

The problem as you have written it is not the same as in the link. This is the version in the link:
\frac{2x^2 + 2x -12}{x - 2}

Factor 2 out of the numerator and then factor the remaining terms into the product of two binomials.

[MeDiCS]

(A little typo :P)
Got it, thanks (quite easy, actually). I first thought of long polynomial division, but that's beyond my current knowledge, plus factoring is faster and easier.