Solve simple rational and radical equations and identify extraneous solutions.
Solve a rational equation by clearing denominators and checking excluded values
Problem
Solve \((x^2~-~4)/(x~-~2)~=~x~+~2\) over its original domain.
Big Picture
What this problem is really about
Preserve the original domain before canceling any common factor. If simplification turns the equation into the same expression on both sides, that identity is true for every input where the cancellation was legal, not automatically for every real input. The canceled factor still records a hole, so its zero remains outside the solution set.
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