Partial Fractions Calculator
Decompose rational expressions into partial fractions. Essential for integration.

Denominator Factors (ax + b)^n

(x +)^
(x +)^
Function Visualization
OriginalDecomposedAsymptotes
Original Expression
(x) / (x - 1)(x + 2)
Partial Fraction Decomposition
0.33/(x - 1) + 0.67/(x + 2)
Decomposed Terms
0.33/(x - 1)Coefficient: 0.333
0.67/(x + 2)Coefficient: 0.667
Verification

Values should match if decomposition is correct

xOriginalDecomposed
000.0005
20.50.4998
-10.50.5005

Partial Fractions Decomposition

P(x)/[(x-a)(x-b)] = A/(x-a) + B/(x-b)
P(x)/(x-a)^2 = A/(x-a) + B/(x-a)^2
Use cover-up method: A = P(a)/Q'(a)

Applications:

  • Integration of rational functions
  • Inverse Laplace transforms
  • Solving differential equations

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