#### Answer

$\color{blue}{(-\infty, 1) \cup (1, +\infty)}$

#### Work Step by Step

The denominator of a rational expression is not allowed to be equal to zero as it will make the expression undefined.
Thus,
$x-1\ne0
\\x \ne1$
This means that the value of $x$ can be any real number except $1$.
Therefore, the domain of the given rational expression is the set of real numbers except $1$.
In interval notation, the domain is:
$\color{blue}{(-\infty, 1) \cup (1, +\infty)}$