Calculadora de Decomposição em Frações Parciais (2 pólos reais distintos)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
(px+q)/((x−a)(x−b)) = A/(x−a) + B/(x−b)
About this calculator
This calculator performs partial fraction decomposition of a rational function of the form (px + q) / ((x - a)(x - b)), where the denominator has two distinct real poles, a and b. The result is expressed as A/(x - a) + B/(x - b), with coefficients A and B computed automatically.
The operation is simple: you enter the values of p, q, a, and b. The calculator then solves the linear system resulting from equating the original expression to the sum of partial fractions. For distinct poles, coefficients are obtained by direct substitution or the Heaviside method.
This tool is useful for students and professionals who need to simplify integrals, Laplace transforms, or differential equations. By decomposing the fraction, calculations such as term-by-term integration become simpler and more straightforward.
Caution: the calculator assumes a and b are different. If they are equal (double pole), the decomposition changes to terms with (x - a)^2. Ensure the poles are truly distinct before using.
Frequently asked questions
What if a and b are equal?
If a = b, the denominator has a double pole. The decomposition would be A/(x - a) + B/(x - a)^2. This calculator does not cover that case.
Can I use complex numbers?
No. This version handles only distinct real poles. For complex poles, the decomposition would involve quadratic denominators.
How does the calculator find A and B?
It solves the linear system from (px+q) = A(x-b) + B(x-a). Substituting x = a and x = b gives A and B directly.
What is partial fraction decomposition used for?
It is mainly used to integrate rational functions, compute inverse Laplace transforms, and solve differential equations.
Is the result always correct?
Yes, as long as the poles are real and distinct. Double-check input values and ensure the fraction is proper (numerator degree less than denominator's).