\(\begin{equation} \lim _{x \rightarrow \infty}\left(\left(\frac{e}{1-e}\right)\left(\frac{1}{e}-\frac{x}{1+x}\right)\ri…

\(\begin{equation}
\lim _{x \rightarrow \infty}\left(\left(\frac{e}{1-e}\right)\left(\frac{1}{e}-\frac{x}{1+x}\right)\right)^x=\alpha, \text { find } \frac{\ln \alpha}{1+\ln \alpha}
\end{equation}\) (22 Jan, Shift II, Memory Based)