Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Decide whether two rational expressions are equivalent
Problem
Are these \(\text{two}\) rational expressions equivalent? \((x^2~-~1)/(x~-~1)\) and \(x~+~1\)
Big Picture
What this problem is really about
To compare rational expressions, separate agreement of values from agreement of domains. Simplify each formula on its allowed inputs, then list every original excluded value and test any input that appears in only one domain. Matching simplified rules mean the values agree where both are defined; equivalent functions also require the domains to match.
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