How to get this expression from the circuit

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SUMMARY

The discussion focuses on deriving the output voltage expression from a circuit where R1 equals R2. The user applied the voltage divider rule, calculating Vout as V_s/2 - Vs[r/(r+1/jwc)], leading to the expression Vout = V_s/2(1 - rjwc/2(rjwc + 1)). Despite multiple attempts, the user was unable to match the expected expression shown in the referenced image.

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nhrock3
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it is given that R1=R2

http://i43.tinypic.com/b8359w.jpg
i used voltage divider
i tried to calculate it by taking v1 as the midle poit of the left brench
and v2 as the middle point of the of the other branch

so Vout=V_s/2 -Vs[r/(r+1/jwc )=v_s/2(1-rjwc/2(rjwc+1))

i can't get the expression in the photo
 
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