I am trying to find the partial fraction decomposition of $ (x^4+2)/(x^5+4x^3)$, which happens to be $(A/x) + (B/x^2) + C/(x^3) + ((Dx+E)/(x^2+6)$. My question is, why is there a " $+E$ " in the final term instead of being just $D$? How do I know when to put a $ + Constant $ in any of the terms?
Thanks!