Partial Fraction Decomposition Calculator

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Partial Fraction Decomposition Calculator

Decompose a rational expression with distinct linear factors and review each coefficient in a clear layout.

Last updated: March 2026 | By ForgeCalc Engineering

Decomposition Solver

Rational functions

Decomposition Steps

1.Numerator: 1x + 2
2.Denominator: (x - 3)(x + 1)
3.Decomposition form: A/(x - 3) + B/(x + 1)
4.Set x = 3: A = 1.25
5.Set x = -1: B = -0.25
Partial Fractions
Expression
1.25/(x - 3) + -0.25/(x + 1)
A
1.25
B
-0.25

What Is Partial Fraction Decomposition?

Partial fraction decomposition rewrites a rational expression as a sum of simpler fractions. It is especially useful for integration and algebraic simplification.

How to Decompose a Rational Expression

  1. Write the numerator and denominator in factored form.
  2. Set up a sum of simpler fractions.
  3. Solve for each unknown coefficient.
  4. Read the decomposed expression in the result panel.
A/(x - a) + B/(x - b), with sign-aware formatting

Worked Example

Example: (x + 2) / ((x - 3)(x + 1)) decomposes into two simple fractions.

A/(x - 3) + B/(x + 1)

Frequently Asked Questions

When can I use this method?

When the numerator degree is less than the denominator degree, or after polynomial division.

What if the roots match?

This simple version requires distinct linear roots.

Does it accept decimals?

Yes. Any finite real coefficients are accepted.

Why is this useful in calculus?

It simplifies integration into basic logarithmic forms.

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