Voltage controlled current source question
Just a note for future reference: You should use the MathJAX tags when writing equations to clean them up!

This is the small signal equivalent model of a degenerated common-source stage:







simulate this circuit &ndash; Schematic created using CircuitLab

Note that the gate is modeled as an open branch, because no current flows into the gate.  Therefore \$ I_g \$ is 0.  We can then write KVL/KCL equations to relate \$ V_s \$ and \$ V_o \$.

If you look at the right side of the circuit, all of the current from the dependent current source flows through \$ R_2 \$. Which means that \$ V_{out} = - g_m V_{gs} R_2 \$  Now, all we need to do is relate \$ V_{gs} \$ to \$ V_s \$.  Note that since no current flows through the resistor, the voltage drop across the resistor is 0.  

So \$V_{gs} = V_s - g_m V_{gs} R_1 \$.  

We can rewrite the above expression as the following

$$
V_s = V_{gs}\left ( 1 + g_m R_1 \right)
$$

Now we substitute \$ V_{gs} \$ into into the equation for \$ V_{out} \$:

$$
V_{out} = \frac{-g_m R_2 V_S}{1 + g_m R_1}
$$
$$
A_v \equiv \frac{V_{out}}{V_s} = \frac{-g_m R_2}{1 + g_m R_1}
$$