I wanted to calculated the inverse fourier transform of the folowing function :

$frac{frac{1}{1+2ipi f}+frac{1}{3+2ipi f}}{frac{2}{1+2ipi f}-frac{2}{4+2ipi f}}$

($f$ is the variable)

I tried the exponential form, Unifying the denominators but in vain, the premitive is still impossible to be found !

can I get some help ? much appreciated.