Frequently Asked Questions
What is partial fraction decomposition?
Writing a rational function P(x)/Q(x) as a sum of simpler rational functions whose denominators are the irreducible factors of Q(x). Each piece is much easier to integrate.
When do I need it?
Whenever you must integrate, Laplace-transform, or series-expand a rational function. It is also useful in control theory and signal processing.
What if the denominator is irreducible?
Use a numerator of the form Mx plus N over the irreducible quadratic. The decomposition still helps even though the piece does not simplify further.
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