Wolfram|Alpha provides broad functionality for partial fraction decomposition. Given any rational function, it can compute an equivalent sum of fractions whose denominators are irreducible. It can also utilize this process while determining asymptotes and evaluating integrals, and in many other contexts including control theory.
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It involves factoring the denominators of rational functions and then generating a sum of fractions whose denominators are the factors of the original denominator. Bézout's identity suggests that numerators exist such that the sum of these fractions equals the original rational function. The process of partial fraction decomposition is the process of finding such numerators. The result is an expression that can be more easily integrated or antidifferentiated.
There are various methods of partial fraction decomposition. One method is the method of equating coefficients. This involves matching terms with equivalent powers and performing algebra to find missing coefficients. It is a common method, and one based on the method of undetermined coefficients. Alternative methods include one based on Lagrange interpolation, another based on residues and more.
The study of partial fraction decomposition is important to calculus, differential equations and other areas, and is also known as partial fraction expansion.