Find the Coefficients of a Partial Fraction Decomposition

numerator coefficients

n

0

-2

n

1

3

n

2

0

number of denominator roots

d

2

3

denominator roots

d

1

1

d

2

-1

d

3

0

help

method

1

2

show solution

Find the coefficients in the partial fraction decomposition.

3x-2

(x-1)x(x+1)

=

A

x-1

+

B

x+1

+

C

x

Multiply the above equation by the common denominator to get:

3x-2 = Ax(x+1)+B(x-1)x+C(x-1)(x+1)

This Demonstration provides simple exercises in partial fraction decomposition. Two methods are used to determine the coefficients in the decomposition. The first consists of equating coefficients of powers of

x

on the left and right sides of the corresponding equation. In the second method, the roots of the denominator are substituted for

x

. In the case of multiple roots, some other value should be substituted.