Partial fractions and linear vs quadratic factors I was watching some videos on partial fraction decompistion and I got confused on one of the examples:
Say for example you have $$\frac{x+4}{x^2(x^2 +3)^2}.$$
The partial fraction equation of this is apparently:
$$\frac{A}{x} +   \frac{B}{x^2} +    \frac{Cx+E}{x^2 +3}   +   \frac{Dx+F}{(x^2 +3)^2}$$
My question is why $A/x+B/x^2$ do not have numerators with an $ax+b$ form, cause $x^2$ is a quadratic not a linear right? Is it because the $x^2$ is in brackets, so you can perceive it as $(x+0)^2$?

hint
if
$$\frac {x+4}{x^2(x^2+3)^2}=\frac {ax+b}{x}+\frac {cx+d}{x^2}+$$
$$\frac {Ax+B}{x^2+3}+\frac {Cx+D}{(x^2+3)^2} $$
$$=a+\frac {b+c}{x}+\frac {d}{x^2}+... $$
then   $x\to +\infty $ gives $a=0$.
