= Solution
In an <operational-amplifier negative feedback> loop, an <operational amplifier> has large <open-loop gain> $A$, with $V_o=A(V_+-V_-)$. Feeding a fraction $\beta V_o$ back to the inverting input opposes an output increase. For a non-inverting <signal> input,
$$
\boxed{\frac{V_o}{V_i}=\frac A{1+A\beta}\simeq\frac1\beta\quad\text{when }|A\beta|\gg1.}
$$
Its sensitivity to <open-loop gain> changes is reduced by $d\ln A_{\rm cl}/d\ln A=1/(1+A\beta)$. Thus <resistor> ratios can set a reproducible gain despite device variation; feedback also suppresses internal distortion and reduces <output impedance>. Gain is traded for usable <bandwidth>, subject to the amplifier's <frequency> response.
For the non-inverting connection, place $R_f$ between output and inverting input and $R_g$ between that input and ground. Then $\beta=R_g/(R_f+R_g)$, giving gain $1+R_f/R_g$. For an inverting connection, ground the non-inverting input, inject the <signal> through $R_{\rm in}$ and return $R_f$ from output to the inverting <node>. Small differential input and negligible input current then give gain $-R_f/R_{\rm in}$. The near-zero <node> is a <virtual ground>, not a physical ground connection.
The feedback must remain stable at the <frequencies> where <loop gain> matters. Extra phase lag can turn the intended opposition into oscillation; adequate <phase margin>, supply headroom, input common-mode range, output-current capability and <slew rate> are required. Feedback neither prevents clipping nor removes all input <noise>.<Operational-amplifier negative feedback by Analog Devices>[Chapter 3, §§3.2.2–3.2.4, gain stability, loop gain and frequency dependence]{ref}
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