Rewrite rational expressions using inspection, polynomial division, or technology.
Rewrite a rational expression by inspection with its original domain
Problem
Rewrite \((x^2~+~3x~+~2)/(x~+~1)\) and state the restriction from its original domain.
Big Picture
What this problem is really about
Inspection works when the numerator can be recognized as the denominator times a simple expression, possibly plus a small remainder. Record the original denominator’s zero before rewriting, then factor or reconstruct the numerator and cancel only on the allowed domain. A zero remainder simplifies the rule, but it does not erase the original excluded input.
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