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Partial Fraction Decomposition Calculator

# Partial Fraction Decomposition Calculator

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Partial fraction decomposition calculator is very useful tool for evaluating a simplified answer into the initial polynomial fraction. This tool uses decomposition rules and formulas. One need to follow the steps only and it helps in finding the result will automatically come out.This tool helps in evaluating polynomials involving different variables. This can be understood by the following examples:-

Example 1:-

Find the Partial fraction decomposition of:-

3x+2 / x2+x

Solution 1:- 3x+2/x2+xNow we know that the denominator is x2+x. Lets factorize it to x(x+1).

Now we write the fraction with one of the factors as the denominator and A and B as unknown numerator. A/x

+ B/x+1So when we add these fractions with the simplified result we get,

3x+2/x(x+1) = A/x + B/x+1;  3x+2=A(x+1)+B(x)

3(x)+2(1)=(A+B)x+A(1);  3=A+B; 2=A;  A=2 and B=1

Example 2:-

Find the Partial fraction decomposition of:-

x2+1/x(x-1)3

Solution 1:- x2+1/x(x-1)3

Now we know that the denominator is x(x-1)3. Now we write the fraction A, B, C and D as unknown numerator.

x2+1/x(x-1)3 = A/(x-1) + B/(x-1)2 + C/(x-1)3 + D/x

x2+1 = Ax(x-1)2 + Bx(x-1) + Cx + D(x-1)3

Let x=1 à 1+1 = 0+0+C+0=C, C= 2; Let x=0 à 1=0+0+0–D, D=-1

Let x=-1; 1+1=-4A+2B+6; 2A–B=2; Let x=2 à 4+1=2A+2B+3; 1=A+B

Answer : A=1, C=2, D=-1

1/(x-1) + 2/(x-1)3 – 1/x