Practice!

Sample Problem

Write the partial fraction decomposition of .

 

Solution

Multiply both sides by (x2+3)2 [the lowest common denominator]

6x3-11x=(Ax+B)(x2+3)+(Cx+D)

6x3-11x=Ax3+Bx2+3Ax+3B+Cx+D

6x3+0x2-11x+0=Ax3+Bx2+(3A+C)x+(3B+D)

Back substitute A=6 into the first equation to find C:

3(6)+C=-11 , 18+C=-11 ,  -29=C

Back substitute B=0 into the last equation to find B:

3(0)+D=0 , D=0

A=6, B=0, C=-29, D=0

So, the partial fraction decomposition is: