How do I find the partial fraction decomposition of 2x(x+3)(3x+1) ?

1 Answer
Sep 23, 2014

2x(x+3)(3x+1)=34x+3143x+1

By decomposing into smaller fractions,

2x(x+3)(3x+1)=Ax+3+B3x+1

by taking the common denominator,

=A(3x+1)+B(x+3)(x+3)(3x+1)

By comparing the numerators,

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

by plugging in x=3,

8A=6A=68=34

by plugging in x=13,

83B=23B=14

Hence,

2x(x+3)(3x+1)=34x+3143x+1