The Point That Goes Missing

A rational expression is a fraction with polynomials on the top and bottom, and it obeys the same law every fraction obeys: the denominator may never be zero. Simplifying such a fraction is a two-part job. You factor and cancel — and you record what the original denominator forbade, because cancelling erases the evidence without changing the rules. Step through each example one line at a time; the graph on the left shows exactly which point goes missing, and why you would never have found it by looking.