I'm a beginner in electrical engineering, and having trouble with this circuit analysis problem. It asks to simplify the circuit into an expression for \$V_L\$ in terms of \$R, R_L,\$ and \$i_S\$.

[![Initial Problem][1]][1]

Here is my work.

[![Handwritten Work][2]][2]

Using Kirchhoff's Laws and Ohm's Law, I get \$i_S = i_1 + i_2\$ and \$V_L = (Ri_1) + (Ri_2)\$. 

Taking the GCF of \$R\$ gets \$V_L = R(i_1 + i_2)\$ therefore \$V_L = Ri_S\$.

Am I doing this correctly? Is there a way to simplify the resistors \$R\$ and \$R_L\$ and know the voltage \$V_L\$? Any help to point me in the right direction is appreciated.


  [1]: https://i.sstatic.net/4AVZb.jpg
  [2]: https://i.sstatic.net/PPanO.jpg