Here is the link for the picture containing the equation
The picture contains a general example of partial fraction expansion for transfer functions (electronic engineering stuff). They substitute in s = jw, but I don't understand how they got rid of so many terms doing this. I have done my own example (the second link provided) but I don't understand how they have effectively gotten rid of the majority of the RHS.
ie. I do not understand how line 3 goes to line 4 in the second link provided. I know I am missing an omega (w) on the LHS (line 1 to line 2) but this doesn't change anything
A clear explanation is appreciated, I am not used to the notation.
Remember that $j^2 = -1$
So in that summation you end up with $-w^2 + w^2$