Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Simplify a rational operation and state all original restrictions
Problem
Fully simplify \((x^2~-~4)/(x~+~2)\) and state its original-domain restriction.
Big Picture
What this problem is really about
Use a stable order for any rational operation: record original restrictions, perform the operation, factor completely, cancel whole common factors, and then restate the restrictions. Terms joined by addition or subtraction cannot cancel until factoring exposes multiplication. Even if the final rule is a polynomial, any canceled original denominator factor still marks a hole.
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