Partial Fraction Decomposition Calculator
Take advantage of the online Partial Fraction Decomposition Calculator to calculate the partial fraction decomposition of any expression. Enter input numerator and denominator of the fraction as input in the specified boxes and hit on calculate to generate output within fraction of seconds.
Partial Fraction Decomposition Calculator: Having knowledge of math concepts will make you strong in attempting all competitive and board exams. On this page, we are giving the each and every step to solve the partial fraction decomposition.
Here, we have provided an example problem for the better understanding of the concept. The step by step guide provided below will make you feel comfortable in solving the fraction. You can easily decompose the fraction with the help of our free hady partial fraction decomposition calculator tool.
How to Perform Partial Fraction Decomposition of Fraction?
Follow these guidelines while solving the partial fraction decomposition of an polynomial expression.
- Take any fraction which is having any number of terms as numerator and polynomial equation as denominator
- First find out the factors of the polynomial equation
- And represent the equation as Variable1/first factor operator variable2/ second factor and so on
- Equate the original expression having factors to the expression obtained in the above step
- Compute the variable values by using the system of linear equation method
- Substitute the variable values to get the partial fraction decomposition of the given fraction.
Example
Question: Perform the partial fraction decomposition of x+7/x2+3x+2?
Solution:
Given fraction is x+7/x2+3x+2
The factors of x2+3x+2 are
x2+3x+2=x(x+1)+2(x+1)
=(x+1)(x+2)
The expression will become
x+7/(x+1)(x+2)
The form of the partial fraction decomposition is
x+7/(x+1)(x+2)=A/(x+1)+B/(x+2)
x+7/(x+1)(x+2)=(x+1)B+(x+2)A/(x+1)(x+2)
The denominators are equal, so equate the numerators
x+7=(x+1)B+(x+2)A=Bx+B+Ax+2A
x+7=x(A+B)+2A+B
The coefficients near the like terms should be equal, so the following system is obtained:
A+B=1
2A+B=7
Multiply A+B=1 with 2
2A+2B=2
2A+B=7
Therefore B=-5
Substitute B=-5 in A+B=1
A=6
The partial fraction decomposition of x+7/x^2+3x+2 is 6/(x+1)-5/(x+2)
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FAQs on Partial Fraction Decomposition Calculator
1. How do you calculate the partial fraction decomposition of a function on a calculator?
The three simple steps to solve the partial fraction decomposition of a function using a calculator are enter the numerator and denominator of the polynomial function in the input section and click on the calculate button to get the expansion fraction.
2. What is partial fraction decomposition?
The process of decomposing the rational expression into smaller rational expressions that we can add or subtract to get the original expression is called partial fraction decomposition.
3. Where is partial fraction decomposition used in real life?
Partial fraction decomposition is used to integrate the rational functions in engineering for finding the Laplace transforms.
4. What does equating coefficients mean?
Equating the coefficients is a method of computing a functional equation of two expressions such as polynomials of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.