Find all $a$ such that $\underset{x\to \mathrm{\infty}}{lim}{\left(\frac{x+a}{x-a}\right)}^{x}=e$

Saw this problem and I thought I'd take a shot at it:

Find all $a$ such that

$\underset{x\to \mathrm{\infty}}{lim}{\left(\frac{x+a}{x-a}\right)}^{x}=e.$

Saw this problem and I thought I'd take a shot at it:

Find all $a$ such that

$\underset{x\to \mathrm{\infty}}{lim}{\left(\frac{x+a}{x-a}\right)}^{x}=e.$