Tips factoring formula to form of $\frac{1}{f(x)}=\frac{1}{g(x)}+\frac{1}{h(x)}+...?$

Question

$$\frac{1}{x^4(x^2+1)}=\frac{1}{x^2+1}-\frac{1}{x^2}+\frac{1}{x^4}$$

I'm having trouble transforming this kind of equation. The goal is to transform the orignal formula to mutiple formulas and keep the numerators = 1.

is there a systematic method to do it?