Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.
Audit an algebraic candidate for equation and context viability
Problem
Candidate \(x~=~2\) comes from a transformed rational equation whose original denominator contains \(x~-~2\). Check the original expression and decide whether to accept the candidate.
Big Picture
What this problem is really about
A solution of a transformed equation is only a candidate for the original one. Recover the original denominator restriction and test the candidate there before doing anything else. If denominator clearing produced a value where the original expression is undefined, reject it for that precise reason rather than attributing the failure to an unrelated operation.
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