Answer
Domain = $\mathbb{R}\backslash\{1\}$ or $\{x\in \mathbb{R}|x\neq 1\}$
Work Step by Step
The domain of a real function ( a function defined on real numbers)
is the set of numbers for which f(x) is defined (for which f(x) can be calculated).
$g(x)=\displaystyle \frac{x^{2}}{x-1}$
can be calculated for any real x, except x=1,
which yields zero in the denominator.
Domain = $\mathbb{R}\backslash\{1\}$ or $\{x\in \mathbb{R}|x\neq 1\}$
