Steps when calculating limits in 2 points

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I am looking for a guideline or hints on how to know if you should check for 2 one-sided limits or one "whole" limit.

I know that when there is an $|x|$ in the denominator that you should check for $x<0$ and $x>0$ and thus (possibly) becoming 2 one sided limits. What other cases require attention for this problem?

(P.S. I only recently started learning about limits)