Deriving a balanced bridge equation

[quaker]

I am having trouble finishing this problem. I am supposed to first derive an equation for V_5 in this circuit:

http://img292.imageshack.us/img292/599/picture3qy2.png

I applied a Delta-Wye transformation to get here:

http://img292.imageshack.us/img292/9672/workot8.jpg

From there I am supposed to show that the circuit is balanced when R1/R2 = R3/R4 for any value of R5. This is where I'm getting stuck. My attempt starts by setting the V5 equation equal to zero and then trying to reduce it. This isn't working very well since the V5 equation is pretty messy to begin with.

Am I going about this correctly, or is there an easier method I should use? Thanks for your help.

 

[doodle]

Yes, I think the V5 equation is messy. But there's an easier way to show the condition for a balanced bridge.

The bridge is balanced if V2 = V4 since there will be no current then across R5. This also means V1 = V3. Then, from applying Ohm's law to the 2 equations and canceling the currents, you should get R1/R2 = R3/R4 quite easily.