Limits and continuity
When substitution gives 0/0, factor and cancel; for a limit at infinity, compare the highest powers.
A worked example
(x² - 25)/(x - 5) is 0/0 at x = 5, but it factors to x + 5, so the limit is 10.
The mistake people actually make
A 0/0 form does not mean the limit fails to exist. It means there is a common factor to remove. A limit only fails when the left-hand and right-hand values disagree.