Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Subtract unlike rational expressions with an LCD and restrictions
Problem
Subtract 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
Build equivalent fractions over the least common denominator before subtracting. Each numerator must receive the factor missing from its own denominator, and the adjusted second numerator stays grouped so the subtraction reaches every term. Simplify the resulting numerator, check for common factors, and keep every zero of the original denominators excluded.
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