Partial fraction question with squared

Question

How could one apply partial fraction decomposition to $$\left(\frac{s}{s^2+4}\right)^2$$

I tried to separate by doing $$\frac{A}{s^2+4} + \frac{B}{s^2+4}$$ and I got strange solution $A+B=0$ and $A+B=1$.

Answer 1

You have assumed the wrong form that the partial fraction will take. Try $$\frac{s^2}{(s^2+4)^2} = \frac{As+B}{s^2+4} + \frac{Cs+D}{(s^2+4)^2}$$ Partial fractions with squares in the denominator always seemed kind of weird to me, but this should get you the result you are after!