Partial Fraction Decomposition Calculator

Looking for a Partial Fraction Decomposition Calculator? In this page, you will find all information that you need to define and calculate partial fractions along with a partial fraction decomposition calculator .

Before we go on talking to what partial fraction calculators, first we need to know what the Partial fractions are?

Partial Fractions Decomposition

Partial fractions and partial fraction calculator image

The partial fraction decomposition or partial fraction expansion of a rational function is an operation that consists of expressing the fraction as a sum of a polynomial and one or several fractions with a simpler denominator.

So, partial fractions are a decomposition process to start with the simplified answers and taking back the final expressions into its initial polymer fractions. For this we need to first decompose the denominator of the fraction. 

After this, you have to write the fractions with one of the factors for each of the denominators. As the numerators are not known, we have to then assign variables (any capital letters) for these unknown values. The result is an expression that can be more easily integrated and non differentiated.

Technical Definition

Let $ R (x) = \dfrac { P (x)} { Q (x)}$ be a rational function, where $ P (x)$ and $ Q (x)$ are expressible as polynomial functions.

Let $ Q (x)$ be expressible as:$ Q (x) = \displaystyle \prod_{k \mathop = 1}^n {q_k} (x)$ where the $ {q_k} (x)$ are themselves polynomial functions of degree at least $1$.

Let $ R (x)$ be expressible as:$ R (x) = r (x) \displaystyle \sum_{k \mathop = 0}^n \dfrac { {p_k} (x)} { {q_k} (x)}$ where:

$ r (x)$ is a polynomial function which may or may not be the null polynomial, or be of degree 0 (that is, a constant) each of the ${p_k} (x)$ are polynomial functions the degree of $ {p_k} (x)$ is strictly less than the degree of $ {q_k} (x)$ for all $k$.

Then $ r (x) \displaystyle \sum_{k \mathop = 0}^n \dfrac { {p_k} (x)} { {q_k} (x)}$ is a partial fractions expansion of $ R (x)$.

Source: Definition: Partial Fractions Expansion – ProofWiki

These partial fractions can be solved using various methods such as Lagrange interpolation and residues . But the smart and new  method to solve it is by using partial fraction calculators.

What is a Partial Fraction Decomposition Calculator?

Partial fraction calculator is an online tool which makes calculations very simple and exciting. This calculator can  decompose any given rational fraction and can generate equivalent sums of fractions whose denominator cannot be reduced. It can too determine asymptotes and evaluate integrals.

How does it work?

This calculator works based on some steps :-

Step 1:- Enter the numerator

Suppose,  $x+7$

Step 2:- Enter the denominator

Eg:- $x^2+3x+2$

Step 3:- Enter ‘calculate’.

After following these steps you will get the solution to your problem. You can also note the steps of the solution and make out how it’s done. 

By looking into these steps you might have figured out how quick this process is . 

But, as we know students do not  need to be fully dependent on these calculators as it can surely make your work easier but can turn out to be during exams. So, trying it yourself is more advantageous than using these techniques as it involves learning , experience and gives the ability to solve more complex sums with greater speed .

However not ignoring the fact that this calculator has a lot to do with it.

Usage of a partial fraction calculator

  • makes our work effortless
  • It doesn’t consume a lot of time.
  • If you are having any queries related to the solution , you can always write it in the comment box in simple English. (to avoid questionable queries do not neglect the use of parentheses where needed).
  • Users can also give any kind of suggestions if they want.
  • Can be used in situations where you want instant solutions.
  • It gives you a step by step solution.

Explore other calculators.