Can you explain the voltage divider in the feedback network?

In the amplifier network shown in the handout, a simple voltage divider with resistors fills the feedback box shown in the generic negative-feedback diagram. If you imagine a power supply $\hat{V}_1$ connected to the $+$ and $-$ inputs of the amplifier, $\hat{V}_4$ in the generic diagram corresponds to $\hat{V}_B$ in the amplifier picture ($\hat{V}_B$ is at the point between $R_f$ and $R_G$). $\hat{V}_4=\hat{F} \hat{V}_3$ then corresponds to $\hat{V}_B = R_G/(R_f+R_G) \hat{V}_{\rm out}$, so $F=R_G/(R_f+R_G)$. You can then choose resistors to make $F= 0.1$ (or some other value $<1$); the reciprocal of it will be your closed-loop gain.