#### Answer

$\left\{x|x\gt 1\right\}$

#### Work Step by Step

The square root is defined only when the radicand (number/expression inside the radical sign) is non-negative.
However, since the square root is in the denominator, its value is not allowed to be zero as it will make the whole expression undefined.
Thus, to find the values of $x$ for which the given expression is defined, solve the inequality $x-1 \gt 0$ to obtain:
$x-1 \gt 0
\\x-1+1 \gt 0+1
\\x \gt 1$
Thus, the domain of the given expression is the set of all real numbers greater than $1$.