Current Divider Formula Proof
Let's define \$G_1=1/R_1\$ and \$G_2=1/R_2\$. These values are conductances, the dual of resistances. 

Now we can restate Ohm's law in terms of conductance: \$I=VG\$. 

Then, the current through conductor #2, \$I_2\$, is \$VG_2\$, and or our two conductors in parallel, the current \$I\$ is \$V\left(G_1+G_2\right)\$.

Now to get \$I_2 / I\$ we just divide:

$$\frac{I_2}{I}=\frac{VG_2}{V(G_1+G_2)}$$

Cancel the V's and convert the G's back to R's and you have your "G rule".