I am studying Analog electronics and am learning about frequency response at the moment. My textbook is good but skips steps sometimes, and I've been trying for too long to fill in the blanks. If someone can show me how the text got from point A to point B and where I'm going wrong, I'd really appreciate it!

The example involves deriving the transfer function for a simple parallel load capacitor circuit

(The attached schematic isn't completely accurate (sorry): the one in the example has an additional resistor Rs in series with the source).

Anyway, the resistor in series with the source is labeled Rs, the resistor in parallel with the capacitor is Rp, and the capacitor is Cp. Vo is taken across the parallel elements.

The book gave something like: from this schematic it can be seen that Vo/Vi = (Rp/(Rs+Rp))*(1/(1+sCp(RsRp/(Rs+Rp))).

My attempt to derive it is as follows:

Node voltage at the output terminal yields

Vo/Rs - Vi/Rs + Vo/Rp + Vo/(1/sCp) = 0

Vo/Vi = (1/Rs) / [(1/Rs) + (1/Rp) + sCp]

since 1/Rs + 1/Rp should end up equaling 1, I got them over a single denominator:

Vo/Vi = (1/Rs) / [(Rp + Rs)/(Rs*Rp) + sCp]

Factoring out the constants shows that this will never yield the book's answer (or I can't see it, one or the other):

Vo/Vi = [(1/Rs^2) + (1/RsRp)][1 / (1 + s((Rp + Rs)/(Rs*Rp)Cp)]

If someone could show me how the book got from node voltage to their transfer function, or where I started going down the wrong path on my calculations, I would really appreciate it! Thanks in advance for the help.