I have an Op-amp that looks like this:

and I am trying to derive this equation for Ix:

\(I_{x} = (V_{s})\frac{R_{1}R_{3}}{R_{x}(R_{1}R_{3} - R_{2}R_{4}) + R_{1}R_{3}R_{4}}\)

Here is what I have so far:

\(V_{-} = (V_{o})\frac{R_{1}}{R{1} + R_{2}}\)
\(V_{-} = V_{+}\)

I1 going through R4 is:

\(I_{1} = \frac{V_{s} - (V_{o})\frac{R_{1}}{R{1} + R_{2}}}{R_{4}}\)

I2 going through R3 is:

\(I_{2} = \frac{(V_{o})\frac{R_{1}}{R{1} + R_{2}} - V_{0}}{R_{3}}\)

Then Ix is:

\(I_{x} = I_{1} - I_{2}\)

I am not sure if this is correct up to here?

 

You are OK so far. There is a very good simplification to be done in the I2 current formula.

Add the equation V+=Ix*Rx and you are good to go.

 

OK I got it thanks for the help.

 

Glad to hear you solved it.