By properties, I mean linearity, shifting, commutativity, etc.

I was hoping to evaluate something like

$F = \dfrac{i\omega-\xi_1}{((i\omega-\xi_2)^2+\xi_3^2)(i\omega-\xi_4)^2+\xi_5^2)}$

by using the results in this table. If not, would it be best to use partial fraction decomposition or is there another method?