Answer
$$\color{blue}{\bf{ (-\infty,0)\bigcup(0, \infty) }}$$
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = x + 1}$ and $\bf{g(x) = x^2}$
and asked to find the $\bf{domain}$ of $\frac{f}{g}$
$\frac{f(x)}{g(x)} = \frac{x + 1}{x^2}$
$x$ can't be zero because $0^2=0$, and division by zero is undefined.
So the domain of $\frac{f}{g}$ is:
$$\color{blue}{\bf{ (-\infty,0)\bigcup(0, \infty) }}$$
