Solution
= Solution
The denominator vanishes only at $x=0$, giving a vertical <asymptote>. Since $1-e^x=-x+O(x^2)$, the <function> tends to $+\infty$ from the left and $-\infty$ from the right. Its <derivative> is
$$
\frac{d}{dx}\frac1{1-e^x}=\frac{e^x}{(1-e^x)^2}>0,
$$
so each branch is increasing. The horizontal <asymptotes> are $y=1$ as $x\to-\infty$ and $y=0$ as $x\to+\infty$. The left branch lies above $1$; the right branch lies below $0$, as in the preceding figure.