Partial fractions with 2 squared terms

Question

Attempting the following partial fraction equation and was wondering how to approach the $s^2$ outside the brackets: $$\frac{1}{s^2(s^2+2s+10)}$$

Answer 1

$$\frac{1}{s^2(s^2+2s+10)}=\frac{A}{s}+\frac{B}{s^2}+\frac{Cs+D}{s^2+2s+10}$$

Now, just cross-multiply and get the values of $A,B,C,D$ in the usual way.

Answer 2

Follow the help given by @Your IDE and the answer will be:

$$\frac{s-3}{50 \left(s^2+2 s+10\right)}+\frac{1}{10 s^2}-\frac{1}{50 s}$$