Decide whether a rewrite changes the domain and identify which restrictions must still be preserved
Problem
Does rewriting \((x^2-4)/(x-2)\) as \(x+2\) change the domain?
Big Picture
What this problem is really about
A rewrite can simplify a formula while making its visible domain look larger. Record every original denominator exclusion first, because canceling a factor only proves equality where that factor was nonzero. To represent the original function, carry the exclusion alongside the reduced formula even if the reduced expression alone accepts that input.
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