Negative feedback can make an op-amp's closed-loop gain depend mainly on external resistors rather than on the very large and uncertain open-loop gain.

For an inverting amplifier, the non-inverting input is grounded, the input reaches the inverting node through $R_{in}$, and feedback returns through $R_f$. With the ideal op-amp conditions,

$$\frac{v_o}{v_{in}}=-\frac{R_f}{R_{in}}.$$

For a non-inverting amplifier, the input is applied to $v_+$ and a resistor divider feeds back a fraction of the output to $v_-$. The gain is

$$\frac{v_o}{v_{in}}=1+\frac{R_f}{R_g}.$$

The special case with unity gain is a voltage follower.

These topologies illustrate the same design principle: strong negative feedback makes the closed-loop behavior depend primarily on the feedback network. The formulas remain valid only while the op-amp can supply the required output without violating its limits.