Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Add rational expressions that already have a common denominator, then simplify and state restrictions
Problem
Add and fully simplify \(3/(x~+~1)~+~5/(x~+~1)\). State the original restriction.
Big Picture
What this problem is really about
When rational expressions already share a denominator, treat them like ordinary fractions with that same denominator. Record its zeros, keep the denominator unchanged, and combine only the numerators according to the operation. After simplifying the new numerator, factor it and the denominator to check for whole common factors, while retaining the original exclusions.
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