What I've learned so far from Navy school is that operational amplifiers are used as a substitute for transistor amplifiers and they contain three main circuits: the differential amplifier, common collector amplifier and the push-pull amplifier. They are represented by a triangle pointing to the right. My question is, why is the voltage gain \$-\frac{R_f}{R_i}\$


![enter image description here][1]


As far as I know, \$R_f\$ provides negative feedback to \$v_{in}\$, but why are we not treating \$R_{in}\$ and \$R_f\$ as part of a voltage divider like a non-inverting amplifier? I can see how they would reason that the incoming current is \$-\frac{v_{in}}{R_{in}}\$ without the voltage divider



  [1]: https://i.sstatic.net/lliw2.gif
  [2]: https://i.sstatic.net/mWGVY.jpg