I have this relatively simple partial fraction
$$\frac{2}{s^2+4} = \frac{As+B}{s^2+4}$$
I multiply each side by $(s^2+4)$ and all that remains is $2 = As + B$. Then can I match the coefficients up and claim $B = 2$ and $A = 0?$ Then this just gives me $\frac{2}{s^2+4} = \frac{B}{s^2 + 4}$. I can't tell if my reasoning is correct or if there is some circular logic that is making my answer wrong, thanks