I can't understand that transition from the solution. Can you help me? How the solution got 1/(B-a) and how is the multiplication removed of the Y(f).

 

Tried the following simplification in Maple; it contains the clue you need.

 

I can't understand that transition from the solution. Can you help me? How the solution got 1/(B-a) and how is the multiplication removed of the Y(f).

Hello there,

That lower result is a partial fraction decomposition of the upper expression.
If you replace j*2*pi*f with just a single variable 's' it makes it a little more clear as then you start with:
[1/(a+s)]*[1/(b+s)]

Try to do a partial fraction decomposition on that and see the result you want pop out
Then just replace 's' with the previous j*2*pi*f and you're done.

 

Thank you! I'm done