Potential Dividers help!

Hi,
I'm revising potential dividers for my physics AS and I've managed to confuse myself looking at potential divider circuits with LDR's in them. I've established that as light intensity increases the resistance falls. This means that the voltage must decrease and so the voltage increases in the other resistor.
However how does this affect the current? Surely the current would be fluctuating for each resistor due to the changing voltages and resistances, although I was under the impression that the current was consistent throughout the circuit?
Also how would you work out the changing voltages, because surely if the current is changing and so is the voltage then the only constant you have is the resistance?
Thanks,
James