I want to find four numbers $a$, $b$, $c$, $d$ of the function $f(x)= \dfrac{a x + b}{c x + d}$ satisfying the conditions $f(-6)=4$, $f(-5)=5$, $f(1)=3$ and $f(2)=2$. I tried
f[x_] := (a x + b)/(c x + d);
Solve[{f[-6] == -4, f[-5] == -5, f[1] == 3, f[2] == 2}, {a, b, c, d}]
But I can not get the result. How to tell Mathematica to do that?