The question is:
((x^2)-4)/ ((x-2)(x+3))
and then cancelling out the x-2 from both the denominator and the numerator leaving me with (x+2)/(X+3)? And then go from there to find the limit?
Yes, you can simplify it that way, but then you need to note that your new Domain is all real numbers with the exception of 2.
Domain = R - {2} is how you would notate it.
Do you understand why? Do you know what makes two equations equilvent?