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\$.

Here is my work.

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.

I'm a beginner in electrical engineering. I am 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\$.

Here is my work:

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 find the voltage \$V_L\$? Any help to point me in the right direction is appreciated.