Rewrite a rational expression by factoring to reveal holes and vertical asymptotes
Problem
Factor and simplify \((x^2~-~1)/(x~-~1)\). State the retained restriction, hole, and any vertical asymptote.
Big Picture
What this problem is really about
Factor both parts of a rational expression before classifying its discontinuities. A denominator factor that cancels leaves its original input excluded but makes the discontinuity removable, so the reduced formula locates the missing point. A denominator factor that remains would instead control a vertical asymptote; if none remains, there is no such asymptote.
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