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: $$\frac{ax+b}{x^2} = \frac{a}{x}+\frac{b}{x^2}.$$ Therefore, $$\frac{A}{x}+\frac{ax+b}{x^2}=\frac{A'}{x}+\frac{b}{x^2}.$$
