Partial fraction decomposition is a procedure used to reduce the degree of either the numerator or the denominator of a rational fraction. This is particularly useful in integrating rational functions and in finding inverse Laplace transforms.
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Pro Tips
The degree of the numerator must be lower than the degree of the denominator.
Factor the denominator completely first.
If there are repeated factors, use multiple terms (e.g., A/(x-r) + B/(x-r)²).
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Fun Facts
"This technique was popularized by Bernoulli and Euler during the development of integration techniques."
"It is a reverse process of finding a common denominator and adding fractions."
