1. The problem statement, all variables and given/known data Is there a number 'a' such that (3x^2 + ax + a + 3) / (x^2 + x - 2) exists as x goes to -2? If so, find the value(s) of 'a' and the limit. 2. Relevant equations The limit rules. Algebra. 3. The attempt at a solution Well... I have absolutely no clue what I'm supposed to do. I suppose I'll have to choose my 'a' values in such a way so the denominator no longer equals zero, *but* other than brute-forcing a-integers in a graphical calculator I have little idea on how to do that. I began by factoring the denominator to (x+2)(x-1), with the hope that I may be able to negate the x+2 somehow, but that didn't work. Then I tried to get (x^2+x-2) in the numerator so the numerator and denominator would cancel out and leave a bit on top, but I couldn't find a way to do that, either. Could someone give me a clue on what approach to try here?