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Partial Fraction Decomposition Calculator
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Partial Fraction Decomposition Calculator (Partial Fractions Calculator) will be helpful to decrease the degree of the given numerator or denominator or both numerator and denominator. Along with the exact form you also get decimal form, percentage form in this calculator. It will also show the solution in a number line and a pie chart.

Below is given a default rational expressions, click "Submit". It will decompose a given rational expression into partial fractions.
 

Steps for Calculating Partial Fraction

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Step 1 :  

Factor the denominator.



Step 2 :  

Write fraction with one of the factors for each denominators and assign variable for each numerator.



Step 3 :  

Multiply through out by denominator factor.



Step 4 :  

Find the variable values.



Step 5 :  

Write the solution as the some of two fraction.



Examples on Partial Fractions Calculator

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  1. $\frac{(6x-3)}{(x^2-x-2)}$


    Step 1 :  

    $(x^2-x-2) = (x-2)(x+1)$



    Step 2 :  

    $\frac{(6x-3)}{(x-2)(x+1)}$ = $\frac{A}{(x-2)}+\frac{B}{(x+1)}$



    Step 3 :  

    $\frac{(6x-3)((x-2)(x+1))}{(x-2)(x+1)}$ = $\frac{A((x-2)(x+1))}{(x-2)}+\frac{B((x-2)(x+1))}{(x+1)}$



    Step 4 :  

    6x-3 = A(x+1) + B(x-2)


    6x-3 = Ax + A + Bx - 2B


    6x-3 = x(A+B) + A - 2B


    A+B = 6.........(2)


    A-2B=-3........(3)


    multiply by 2 in equation (2) and add equation (3)


    2A + 2B = 12


    A - 2B = -3


    -------------


    3A = 9


    A =3


    substitute A value in equation (1)


    3+B=6


    B=3



    Step 5 :  

    substitute A and B value in equation (1)


    $\frac{(6x-3)}{(x^2-x-2)}$ = $\frac{3}{(x-2)}+\frac{3}{(x+1)}$



    Answer  :  

    $\frac{(6x-3)}{(x^2-x-2)}$ = $\frac{3}{(x-2)}+\frac{3}{(x+1)}$



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