I need help with a stupid webassign problem. It's about partial fraction

Question

The question is following:

Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. $$\frac{1}{x^2+x^4}$$

I know how to solve this. but the problem is I have to do it like the example and I can't figure out what the "proper way" the Webassign is looking for.

$$\frac{x^3+x^2+1}{x(x-1)(x^2+x+1)(x^2+1)^3}=\frac{A}{x}+\frac{B}{x-1}+\frac{Cx+D}{x^2+x+1}+\frac{Ex+F}{x^2+1}+\frac{Gx+H}{(x^2+1)^2}+\frac{Ix+J}{(x^2+1)^3}$$

Answer 1

Is it $$\frac A {x^2}+\frac B{x^2+1}$$?

No, it's

$$\frac A{x}+\frac B {x^2}+\frac C{x^2+1}$$

Answer 2

Hint.

Your fraction is equal to $$ \frac{1}{x^2(x^2+1)} $$ and $x^2+1$ is an irreducible quadratic factor.