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Calculation Machine

Partial Fraction Decomposition Calculator

Split a fraction over (x-p)(x-q) into two simple fractions.

Reviewed by James Whitfield · How we check our maths

Your values

ⓘ Live results

Results
A
1.6667
B
-1.6667
Decomposition
1.6667/(x-1) + -1.6667/(x--2)

Quick answer

A = N(p)/(p-q) and B = N(q)/(q-p) for a linear numerator N(x), using the cover-up method.

The formula

A/(x-p) + B/(x-q)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Numerator slope (0 if constant)0
  • Numerator constant5
  • Root p1
  • Root q-2

Result

  • A1.6667
  • B-1.6667
  • Decomposition1.6667/(x-1) + -1.6667/(x--2)

How to use the Partial Fraction Decomposition Calculator

  1. 1Enter the numerator as a linear expression (or a constant if the slope is 0).
  2. 2Enter the two distinct roots p and q of the denominator.
  3. 3The cover-up method gives A and B directly.

Frequently asked questions

What if p equals q?

The denominator has a repeated root, which needs a different decomposition form (A/(x-p) + B/(x-p)^2).

Can the numerator be quadratic?

This tool handles a linear numerator; quadratic numerators need an extra term.

About this calculator