Partial Fraction Decomposition Calculator

Your details

Choose the factored form of your denominator to determine how many unknowns appear.
Coefficient of x in the numerator. For a linear numerator px+q, enter p here.
Constant term in the numerator.
The value a in the first linear factor (x+a). For (x-2), enter -2.
For two-linear/three-linear: the value b in (x+b). For lin-quad: coefficient of x in the quadratic x²+bx+c.
Constant A
1.3333

Numerator of the first partial fraction.

Constant B3.6667
Decomposition4/3/(x+1) +11/3/(x-2)
A1.3333
B3.6667
C-
D-

Decomposition: 4/3/(x+1) +11/3/(x-2)

  • The denominator has two distinct linear factors, which determines the template used.
  • The cover-up method (substituting the root of each factor) is the fastest route for linear factors.
  • For the quadratic term, matching coefficients of each power of x is the reliable approach.
  • You can verify the result by combining the partial fractions back over a common denominator.

Next stepUse this decomposition to integrate the original rational function term by term, or to apply inverse Laplace transforms in control theory.

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