Yes I definitely would evaluate the limits at each end. I was wondering if there are any rules or patterns in the rational function before being evaluated that might tip this behavior off.
Regarding the 2nd part of my post, I figured it out :)
Is there a way to distinguish between rational functions that have the same limit at both ends and those that don't? I think I might have answered my own question, but let's say I evaluate a rational function, and it turns out to be a coefficient ratio with no variables (3/2). Does that mean...