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Partial Fraction Decomposition Calculator

Find partial fractions step by step

This online calculator will find the partial fraction decomposition of the rational function, with steps shown.

Enter the numerator:

Enter the denominator:

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Solution

Your input: perform the partial fraction decomposition of 11x2

Simplify the expression: 11x2=1x21

Factor the denominator: 1x21=1(x1)(x+1)

The form of the partial fraction decomposition is

1(x1)(x+1)=Ax+1+Bx1

Write the right-hand side as a single fraction:

1(x1)(x+1)=(x1)A+(x+1)B(x1)(x+1)

The denominators are equal, so we require the equality of the numerators:

1=(x1)A+(x+1)B

Expand the right-hand side:

1=xA+xBA+B

Collect up the like terms:

1=x(A+B)A+B

The coefficients near the like terms should be equal, so the following system is obtained:

{A+B=0A+B=1

Solving it (for steps, see system of equations calculator), we get that A=12, B=12

Therefore,

1(x1)(x+1)=12x+1+12x1

Answer: 11x2=12x+1+12x1