I have encountered a problem I have been given that I cannot solve. The problem is:

lim(x->2) {1/(x-2) - 1/(x^2-4) }

After a good couple of hours of trying to manipulate the expression to see if I could solve it, I got frustrated and graphed the function, and realized that the limit does not exist.

To save such frustration in the future, is there any way of determining from an expression if the limit actually exists, before trying to solve it?