Partial fractions of 1/(x² − 5x + 6)
Decompose a rational function into a sum of simpler fractions.
Solution
- Numerator 1
- Denominator x² − 5x + 6
- Discriminant of denominator Δ = 1
- Roots of denominator x₁ = 3, x₂ = 2
- Coefficients A = P(3)/(a·(x₁−x₂)) = 1, B = P(2)/(a·(x₂−x₁)) = -1
- Decomposition 1 / (x² − 5x + 6) = 1 / (x − 3) − 1 / (x − 2)
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