Determine real numbers a,b and c such that they verify a certain equation 
up to this point I've determined c this way:

The issue here is that I cannot figure out how to proceed the same way with the other two variables a and b. Is there something I'm missing from the start? Sorry if it's hard to understand I can elaborate if necessary.

Hint:
$$\frac{ax+b}{x^2+1}+\frac{c}{x} = \frac{ax^2+bx+cx^2+c}{x^3+x}$$ and you want this to be $$\frac{x+1}{x^3+x}$$
