Current division into three branches
Hint:
I think the sensible approach is to simplify the circuit far enough to only have 2 branches, then calculate the current through them. Once you know the current, you can focus on the more simplified branch (but now knowing how much current flows through it as a whole), split it into two R's again and apply the familiar rule. 

Full answer:


First of all you should know how one can simplify resistor circuits (reference).
Most people like to draw the circuit in a more suggestive way; grouping R's that are parallel and such. 







simulate this circuit &ndash; Schematic created using CircuitLab


Group R1, R2, R4, R5 and R6


begin with (R1 || R4) = R7; ie. 1/R7 = 1/R1 + 1/R4
(R7 + R2) = R8
R9 = (R8 || R5)
R10 = (R9 + R6) 

Calculate current; now you know the current over R10 and R3
Take R10 and calculate current between R8 and R5