Write the partial fraction decomposition of .

Multiply both sides by
(x^{2}+3)^{2} [the lowest common denominator]

6x^{3}-11x=(Ax+B)(x^{2}+3)+(Cx+D)

6x^{3}-11x=Ax^{3}+Bx^{2}+3Ax+3B+Cx+D

6x^{3}+0x^{2}-11x+0=Ax^{3}+Bx^{2}+(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: