Transfer function of this opamp circuit
I think that you have a sign error in transition from the first to the second line:

$$\begin{eqnarray}
\left[\frac{-R_4}{R_3+R_4}\frac{R_5}{R_5+R_7} + \frac{R_4}{R_3+R_4} \right] V_R &amp;= &amp; \left[-\frac{R_5}{R_5+R_7} + 1 \right]  \frac{R_4}{R_3+R_4}V_R\\
&amp;=&amp; \left[\frac{R_7}{R_5+R_7}\right]\frac{R_4}{R_3+R_4}V_R\\
\end{eqnarray}$$