Need help finding limit $\lim \limits_{x\to \infty}\left(\frac{x}{x-1}\right)^{2x+1}$ Facing difficulty finding limit
$$\lim \limits_{x\to \infty}\left(\frac{x}{x-1}\right)^{2x+1}$$
For starters I have trouble simplifying it
Which method would help in finding this limit?

$\lim_{x\to\infty}(\frac{x}{x-1})^{2x+1}=\lim_{x\to\infty}(\frac{x-1+1}{x-1})^{2x+1}=\lim_{x\to\infty}(1+\frac{1}{x-1})^{2x+1}=e^{\lim_{x\to\infty}\frac{2x+1}{x-1}}=e^2$.
