Examine what happens to the function at the outer points of the domain (be they plus or minus infinity or set values for x) and if necessary differentiate to find maxima/minima as well. For functions such as these looking at the asymptote is also probably necessary, although it just so happens that 2 is already the lower limit of the function (although x does not ever equal 2 of course) in this case so you will do that anyway. Drawing a graph can also be of great assistance.
For fractional functions like this, when you're looking at x tending to infinity, a simple trick is to get rid of the constants - a crude way of understanding this would be to say that infinity + c is still infinity (thinking of infinity is a number is never pleasant but oh well). So in this case you could get rid of the -3 and -2 to find out what the function is approaching as x tends to infinity. Also look at what is happening when x tends to 2, and in this case (as drawing a graph will confirm) there are no turning points to consider, so looking at the domain boundaries alone should guide you to the answer.