Partial Fractions

Split a rational expression into simpler fractions, the key step before integrating, with the setup and coefficient solving shown. Try “partial fractions of (3x + 5)/((x − 1)(x + 2))”.

Try an example:

How the Partial Fractions works

  1. Factor the denominator and write one fraction per factor (A/(x − 1) + B/(x + 2)).
  2. Multiply through by the full denominator and match coefficients or substitute convenient x values.
  3. Solve for the constants and write the decomposition.

Frequently asked questions

What if the numerator’s degree is too high?

Do polynomial long division first so the remaining fraction has a numerator of lower degree than the denominator.

How do repeated factors work?

A factor (x − a)² needs two terms: A/(x − a) + B/(x − a)².

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