Inverse Laplace Transform, am stuck simplifying

Question

I want to find the inverse Laplace transform of $F(s)= \frac{4s}{(s^2+5)^2-4s^2}$, but I'm having trouble simplifying this fraction so I'm able to take the Laplace transform.

I simplified the denominator and got $s^4+6s^2+25$, but I'm not sure how that helps me.

I also tried looking at $4s^2$ and $(2s)^2$, but still am stuck.

Any suggestions?

Answer 1

Hint

$$\frac{4 s}{\left(s^2+5\right)^2-4 s^2}=\frac{4s}{(s^2+5+2s)(s^2+5-2s)}=\frac{As+B}{s^2+5+2s}+\frac{Cs+D}{s^2+5-2s}$$