# What are the asymptote(s) and hole(s), if any, of  f(x) =(1+1/x)/(1/x)?

The is a hole at $x = 0$.
$f \left(x\right) = \frac{1 + \frac{1}{x}}{\frac{1}{x}} = x + 1$
This is a linear function with gradient $1$ and $y$-intercept $1$. It is defined at every $x$ except for $x = 0$ because division by $0$ is undefined.