Non-inverting op-amp amplifier gain as open-loop gain goes to infinity (limit calculation)
Just follow the following approach:

$$\begin{align*}
&amp;= \lim_{A\rightarrow\infty}\frac{A}{1+A\frac{R_1}{R_1+R_F}}\\\\
&amp;= \lim_{A\rightarrow\infty}\frac{A}{1+A\frac{R_1}{R_1+R_F}}\cdot\frac{\frac{1}{A}}{\frac{1}{A}}\\\\
&amp;= \lim_{A\rightarrow\infty}\frac{1}{\frac{1}{A}+\frac{R_1}{R_1+R_F}}\\\\
&amp;= \frac{1}{\frac{R_1}{R_1+R_F}}\\\\
&amp;= \frac{R_1+R_F}{R_1}\\\\
&amp;= 1+\frac{R_F}{R_1}
\end{align*}$$