[![enter image description here](https://i.stack.imgur.com/3M7X3.png)](https://i.stack.imgur.com/3M7X3.png)

Here's what I did. I know it's wrong but I cannot figure out why.

Let \$V\_s\$ be the voltage at the node between R2, R3 and R4.

From the ground to \$V\_o\$ terminal there is a voltage \$V\_o\$ which
is divided over R3 and R4 in such a manner: \$V\_s=\frac{V\_o R4}{R3+R4}\$

Is this correct?

From the ground to \$V\_i\$ terminal there is a voltage \$-V\_i\$ which
is divided over R1, R2 and R4 in such a manner: \$V\_s=\frac{-V\_i R4}{R1+R2+R4}\$

Is this correct?

Now equating the above two equations one gets the wrong answer for \$\frac{V\_o}{V\_i}\$. The correct approach uses a Thevenin simplification.

I understand the Thevenin approach but what am I doing wrong here?