Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Add unlike rational expressions with an LCD and domain restrictions
Problem
Add and fully simplify \(1/x~+~1/(x~+~1)\) using a least common denominator. State the original restrictions.
Big Picture
What this problem is really about
For unlike denominators, factor first and build the least common denominator from every required factor at its highest power. Record all original denominator zeros, then multiply each fraction by only the factors it is missing. Once the denominators match, combine the adjusted numerators and factor again before deciding whether anything cancels.
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