## Introduction to Partial Fraction Decomposition Calculator

Partial Fraction Decomposition Calculator with steps is an online tool that helps you to **find the rational expression** in simple fractions.

Partial Fractions Calculator determines the function whose denominator exponential power is higher than its numerator exponential power into a simple fraction in a few seconds.

## What is Partial Fraction Decomposition?

Partial fraction decomposition is an algebraic expression in calculus in which the rational function decomposes into a **sum of two or more rational functions**. This method is used for that rational function whose numerator degree is greater than the denominator degree.

## Formula Used by Partial Fraction Calculator with Steps

In Partial fraction decomposition P(x), and Q(x) are two polynomial functions whose **p(x) degree is less than Q(x)**. The partial fraction decomposition calculator uses the following formula,

\begin{array}{rrr|r} ax & + & b & \frac{A}{ax+b} \\ ax & + & b^k & \frac{A_1}{ax+b} + \frac{A_2}{(ax+b)^2} + ... + \frac{A_k}{(ax+b)^k} \\ & ax^2 & bx + c & \frac{A^x + B}{ax^2 + bx + c} \\ (ax^2 &+ bx + & c)^k & \frac{A_1x + B_1}{ax^2 + bx + c} \frac{A_2x + B_2}{(ax^2 + bx + c)^2} +... + \frac{A_kx + B_k}{(ax^2 + bx + c)^k}\end{array}

$$ f(x) \;=\; \frac{P(x)}{Q(x)} $$

F(x) is the function with the x variable

P(x),Q(x) is the two polynomial functions

## How Does the Partial Fractions Calculator Work?

Partial Fraction Calculator with steps has an advanced feature that enables you to solve various types of rational expressions in the run of time. You can add that polynomial function whose numerator degree is greater than the denominator degree for partial fraction decomposition solutions.

When you enter the algebraic function in the partial fraction expansion calculator, it will analyze the function. After checking the function behavior, if the denominator expression is in a quadratic equation then factorize it so that it becomes a simple function.

Then partial decomposition calculator **decomposes the denominator expression** in two or more than two fractions and in the numerator adds A, B, C… values respectively as per the partial fraction formula.

The pfd calculator takes the LCM of the denominator expression and then multiplies the LCM on both sides of the equation. For the value of A, B… put x+c=0 and put x value on both sides of the equation.

After adding the x value partial fraction solver gives you the **value of A or B**. Sometimes x value does not give the solution of the root value then it compares the x coefficient of both sides of the equation then you get A+B=0, A-B=3.

After obtaining the equation our calculator gives you the values of A, and B, and substitutes the root value into the above equation.

Let's elaborate an example along with the solution related to Partial Fraction Decomposition to understand the working mechanism of our partial fractions solver.

## Solved Example of Partial Fraction Decomposition

The partial fraction decomposition calculator with steps can give accurate answers in some seconds but it’s crucial to understand each step manually so an example is given below,

### Example:

Decompose the following rational expression using the distinct linear factors.

$$ \frac{3x}{(x+2)(x-1)} $$

**Solution:**

Let's decompose the denominator expression and numerator with A, B

$$ \frac{3x}{(x+2)(x-1)} \;=\; \frac{A}{(x+2)} + \frac{B}{(x-1)} $$

Now, multiply the denominator value on both sides of the equation to reduce the fraction

$$ (x+2)(x-1) \biggr[ \frac{3x}{(x+2)(x-1)} \biggr] \;=\; (x+2)(x-1) \biggr[ \frac{A}{(x+2)} \biggr] + (x+2)(x-1) \biggr[ \frac{B}{(x-1)} \biggr] $$

New expression after the elimination of the partial fraction. Then put x-1=0 in a simple expression.

$$ 3x \;=\; A(x - 1) + B(x + 2) $$

$$ 3(1) \;=\; A[(1) - 1] + B[(1) + 2] $$

$$ 3 \;=\; 0 + 3B $$

$$ 1 \;=\; B $$

You get the value of B. For A value put x+2=0 in the simple expression.

$$ 3x \;=\; A(x-1) + B(x+2) $$

$$ 3(-2) \;=\; A[(-2) -1] + B[(-2) + 2] $$

$$ -6 \;=\; -3A + 0 $$

$$ \frac{-6}{-3} \;=\; A $$

$$ 2 \;=\; A $$

Now we get the value of A and B , put it in the above expression

$$ \frac{3x}{(x+2)(x-1)} \;=\; \frac{2}{(x+2)} + \frac{1}{(x-1)} $$

## How to Use the Partial Fraction Decomposition Calculator?

Partial fraction calculator has the simplest design so you can use it to calculate the rational expression problems with the direct division method or decompose the function into a smaller fraction in less than a minute.

Before adding the input value into the Partial fractions calculator, you must check out some simple steps only for the evaluation process. These steps are:

- Enter the
**numerator value of the rational function**in partial decomposition calculator input box. - Enter the denominator value of the rational function in the input box
- Review your input algebraic function before the evaluation process in the calculator
- Click the “Calculate” button to get the desired result of your given rational expression problem.
- Click on the “Recalculate” button to get a refresh page for solving more partial fraction problems solutions.

## Output from Partial Fraction Expansion Calculator

Partial Fraction Decomposition Calculator with steps gives you the solution to the polynomial rational function when you add the input into it. It provides you with **solutions with a complete process** in no time. It may contain as

**Result option**

This option gives you a solution for the Partial Fraction Decomposition problems

**Possible steps**

This option provides you with all the steps for the solving Partial Fraction Decomposition problem

## Advantages of Partial Decomposition Calculator

Partial fraction expansion calculator will give you tons of **benefits whenever you use** it to calculate algebraic rational expressions without using the direct division method.

You just need to enter a partial fraction in the input field and the rest of the work will be done in the pfd calculator automatically. Its benefits are:

- Our partial fraction solver saves time from doing lengthy and complex calculations of rational function problems and their solutions
- Partial fraction calculator with steps is a free tool as it does not demand you to pay the fee for the evaluation of the given polynomial function for partial fraction functions.
- Partial fractions solver is an easy-to-use tool as it can operate from a laptop, desktop, and mobile device.
- The simple layout of partial fractions calculator makes it easy for everyone that they can use it to calculate the various types of partial fraction problems easily.
- The partial fraction decomposition calculator with steps is a
**trustworthy tool**as it instantly provides accurate solutions to Partial Fraction Decomposition problems