Factor the numerator and denominator, cancel common factors, and state domain restrictions — the values of x that make the original denominator equal to zero.
Factor completely first, then cancel common factors
A rational expression simplifies when the numerator and denominator share a common factor. The key rule: you can only cancel entire factors (things multiplied), never individual terms (things added or subtracted).
After simplifying, the domain restrictions from the original denominator still apply — even for values that were cancelled. The simplified form is undefined at those x-values too.
Process: (1) Factor the numerator. (2) Factor the denominator. (3) Identify common factors. (4) Cancel them. (5) State all x-values that make the original denominator = 0.
Cancelled factor → hole (removable discontinuity)
When a factor cancels from both numerator and denominator, it creates a hole (removable discontinuity) in the graph — a single missing point — at that x-value, not a vertical asymptote.
A vertical asymptote occurs when the denominator of the simplified form equals zero (a factor that was NOT cancelled).
One-on-one Algebra 2 tutoring makes factoring and domain restrictions click — we work through your actual problems and build the intuition that sticks for tests and beyond.