Find where the denominator of the rational function equals zero.
Exclude any factors that cancel with the numerator (holes/removable discontinuities).
For each remaining denominator factor that is zero, record the corresponding (x)-value as a vertical asymptote.
If the function is not rational, identify points where the function approaches (pminfty) (e.g., from one-sided limits).
Use one-sided limits to confirm:
Compute (lim_{xto a^-} f(x)) and (lim_{xto a^+} f(x)).
If either limit is infinite (or both diverge), then (x=a) is a vertical asymptote.
Check for endpoints of the domain (vertical asymptotes can occur at domain boundaries if the function diverges there).