partial fraction decomposition of $\frac{(2l+1)(l+1)}{K+(l+1)(l+2)(l-1)}$

Question

I am struggling with the partial fraction decomposition of

$$\frac{(2l+1)(l+1)}{K+(l+1)(l+2)(l-1)},$$

where $K$ is a positive real number.

I would like to decompose it in a sum of simpler polynomial fractions.

I tried the Mathematica's function "Apart" but it is returning the fraction so I am thinking there is no simple partial fraction decomposition.

Could you help me?

Answer 1

i think the simpliest form is this here $${\frac {2\,{l}^{2}+3\,l+1}{{l}^{3}+2\,{l}^{2}+K-l-2}}$$