Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Add rational expressions by factoring, simplifying, and stating denominator restrictions
Problem
Add and fully simplify \(1/(x~-~2)~+~3/(x~+~1)\). State the original restrictions.
Big Picture
What this problem is really about
Factor the denominators before constructing the least common denominator, and record every original denominator zero. Rewrite each fraction by multiplying its numerator and denominator by exactly the missing factors, then combine the adjusted numerators with careful distribution. Only after that sum is simplified should you test the numerator for factors shared with the LCD.
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