Pulse train rect function

Question

Why $ X_\delta (f) = \frac{4A}{3} ( 1 - \frac{1}{2} rect \frac{f}{B} ) $ is equal to The $ X_\delta (f) $ signal I wrote here ? my book obtained the same equation I wrote on the paper but , before doing the convolution to obtain the rebuilt signal , it change the rect signal ( that we both obtained ) to the first I wrote initially ..