Partial Fraction Decomposition (2 distinct linear)
P(x) / [(x−a)(x−b)] = A/(x−a) + B/(x−b). Distinct linear factors only.
Result
Decomposition
2.0000/(x−1) + -1.0000/(x−-2)
A = P(a)/(a−b); B = P(b)/(b−a).
- Numerator P(x)1x + 5
- Denominator(x − 1)(x − -2)
- P(a)6.000000
- P(b)3.000000
- A2.000000
- B-1.000000
Step-by-step
- A = P(a) / (a − b) = 6.0000 / (1 − -2) = 2.0000.
- B = P(b) / (b − a) = 3.0000 / (-2 − 1) = -1.0000.
How to use this calculator
- Enter linear numerator + 2 distinct roots.
About this calculator
Partial fraction decomposition splits a rational function into simpler fractions. For (px+q) / [(x−a)(x−b)] with distinct a, b: A = P(a)/(a−b), B = P(b)/(b−a). Used in integration (each simpler fraction has known antiderivative ln(x−c)) and Laplace transforms. For repeated factors, irreducible quadratics, or higher-order: more complex algorithms (cover-up method extended). Source: Wolfram MathWorld - Partial Fraction Decomposition.
Frequently asked
To integrate or transform. ∫1/(x−a) dx = ln|x−a|. Each piece becomes elementary.
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