Partial Fractions Decomposition Calculator


With this calculator, you can find the partial fractions of the rational expression entered. The expression has to be entered correctly for the calculator to generate the answer.

How to use the partial fraction calculator?

Step 1: Enter the algebraic expression in the corresponding input box. Consider the aspects mentioned in the following question to enter the expression correctly.

Step 2: Enter the main variable of the expression in the second input box. In most cases, the variable is x.

Step 3: Click on “Calculate” to obtain the partial fractions of the entered expression.

Step 4: The partial fractions along with the original expression will be displayed at the bottom.

How to enter expressions in the calculator?

To enter expressions into the calculator, we must use * to indicate multiplication between coefficients and variables. That is, instead of entering 4x or 5x^2, we have to write 4*x or 5*x^2.

Also, we must use the ^ sign to indicate an exponent. For example, we write 3*x^3 or 5*x^2 to indicate that x is cubed and squared, respectively.

Finally, we can write fractions using the / sign and parentheses to indicate the fraction correctly. The following are some examples of how to enter expressions correctly:

  • To write \(\frac{3x^2+1}{2x^2-x+2}\), enter (3*x^2)/(2*x^2-x+2) and the variable x.
  • To write \(\frac{x^2+2}{x(x-1)^3}\), enter (x^2+2)/(x*(x-1)^3) and the variable x.

What are partial fractions?

Finding partial fractions is an operation that consists of expressing a fraction as the sum of a polynomial and one or more fractions with a simpler denominator.

Why find partial fractions?

Partial fractions allow us to rewrite a complex algebraic fraction into simpler fractions. This is particularly useful when we want to find the integral of the fraction since integrating the partial fractions is relatively easy.

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