eqns={((u1-uminus)/R1)+((uout-uminus)/R2)==0,uplus==uout*(R4/(R4+R3)),uout==A*(uplus-uminus)};

output=uout/.Solve[eqns,{uout,uminus,uplus}][[1]]

Limit[output,A->∞]

eqns={((u1-uminus)/R1)+((uout-uminus)/R2)==0,uplus==0,uout==A*(uplus-uminus)};
output=uout/.Solve[eqns,{uout,uminus,uplus}][[1]]
Limit[output,A->∞]

A=(10^5);
USat=12;
f[uplusMinusUMinus_]:=USat*Tanh[(A/USat)*uplusMinusUMinus];
Plot[{f[Δu],A*Δu},{Δu,-2*(10^(-4)),2*(10^(-4))},PlotRange->All,PlotStyle->Thick,AxesLabel->{"(SuperPlus[u])-(SuperMinus[u])[V]","uV[V]"}];

R2=10*(10^3);
R1=(10^3);
eqns={((u1-uminus)/R1)+((uout-uminus)/R2)==0,uout==f[uplus-uminus]}/.uplus->0

eqnOfOneVar

Solve[eqns[[1]],uminus][[1]];
eqnOfOneVar=eqns[[2]]/.%;
outpu[u11_]:=uout/.FindRoot[eqnOfOneVar/.u1->u11,{uout,1}];
outpu[10.]

Plot[outpu[1.5Sin[t]],{t,0,2Pi}]