Partial Fractions Calculator
Two Distinct Linear Factors
Decompose (px + q) / ((x - a)(x - b)) into A/(x-a) + B/(x-b)
Repeated Linear Factor
Decompose (px + q) / (x - a)² into A/(x-a) + B/(x-a)²
Linear + Irreducible Quadratic
Decompose N / ((x - a)(x² + bx + c)) format
Formula
Distinct linear: A/(x-a) + B/(x-b) | Repeated: A/(x-a) + B/(x-a)² | Irreducible quadratic: (Bx+C)/(x²+bx+c)
Frequently Asked Questions
What is partial fraction decomposition?
Partial fraction decomposition breaks a complex rational expression into simpler fractions. For example, (3x+5)/((x-1)(x+2)) = A/(x-1) + B/(x+2). It's essential for integration of rational functions and inverse Laplace transforms.
When do you use partial fractions?
Use partial fractions when integrating rational functions, computing inverse Laplace transforms, or simplifying transfer functions in control theory. The denominator must be factorable into linear and/or irreducible quadratic factors.
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