Rewrite functions in equivalent forms to reveal and explain useful properties.
Decide whether a proposed rewrite keeps the same function and the same restrictions
Problem
Does this rewrite preserve the original restrictions: \((x^2-4)/(x-2)\) rewritten as \(x+2\)?
Big Picture
What this problem is really about
Cancellation preserves the outputs only where the original rational expression is defined. Record the denominator restriction before simplifying, then compare that restricted line with the unrestricted linear function. The missing input creates a hole, so matching formulas almost everywhere do not automatically define identical functions.
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