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:

What you can do with the Partial Fractions

Split rational expressions into simpler fractions.

Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.

Example input

e.g. partial fractions of (3x + 5)/((x - 1)(x + 2))

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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