How to Solve for Variables in Equations with Multiple Variables and Equations?

[proto]

$$\frac{1}{x^3(x^2+1)}=\frac{ax^2+bx+c}{x^3}+\frac{dx+e}{x^2}\\$$
$$ax^4+bx^3+cx^2+dx^4+ex^3=x^4(a+d)+x^3(b+e)+cx^2=1\\$$
$$c=0\\$$
$$b+e=0\\$$
$$a+d=0\\$$

i got 4 variables with 2 equations

what to do??

 

[g_edgar]

$$\frac{1}{x^3(x^2+1)}=\frac{ax^2+bx+c}{x^3}+\frac{dx+e}{x^2}\\$$
$$ax^4+bx^3+cx^2+dx^4+ex^3=x^4(a+d)+x^3(b+e)+cx^2=1\\$$
$$c=0\\$$
$$b+e=0\\$$
$$a+d=0\\$$

i got 4 variables with 2 equations

what to do??

$$\frac{1}{x^3(x^2+1)}=\frac{ax^2+bx+c}{x^3}+\frac{dx+e}{x^2+1}\\$$