\displaystyle v_e=-v_1

\displaystyle \frac{v_s-v_1}{R_1}=\frac{v_1}{R_1}+\frac{v_1-v_o}{R_2}

\displaystyle \frac{v_1-v_o}{R_2}=\frac{v_o-A_0v_e}{R_o}=\frac{v_o+A_0v_1}{R_o}

\displaystyle \frac{v_o}{v_s}=-\frac{\dfrac{R_2}{R_1}}{1-\left(\dfrac{1}{R_1}+\dfrac{1}{R_i}+\dfrac{1}{R_2}\right)\left(\dfrac{1}{R_2}+\dfrac{1}{R_o}\right)\Big/\left(\dfrac{A_0}{R_2}-\dfrac{R_o}{R_o}\right)\dfrac{1}{R_2}}

\displaystyle \frac{v_o}{v_s}\simeq-\frac{\dfrac{R_2}{R_1}}{1+\left(\dfrac{1}{R_1}+\dfrac{1}{R_i}+\dfrac{1}{R_2}\right)\dfrac{1}{\dfrac{A_0}{R_oR_2}}\dfrac{1}{R_o}}

\displaystyle \frac{v_o}{v_s}=-\frac{\dfrac{R_2}{R_1}}{1+\left(\dfrac{1}{R_1}+\dfrac{1}{R_i}+\dfrac{1}{R_2}\right)\dfrac{R_2}{A_0}}

\displaystyle \frac{v_o}{v_s}=-\frac{4}{3}