## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

The domain is $\{x\in \mathbb{R}|x\gt1\}$.
Requirement (1) For a fraction to be defined, the denominator can not be equal to $0$. Thus, $x-1\ne0$ $x\ne1$ Requirement (2) For a square root to be defined, the expression inside the radical must be greater than or equal to $0$. Thus, $\frac{2}{x-1}\geq0$ As the nominator will always be positive, the denominator should also be positive. $x-1\gt 0$ $x\gt1$ The two requirements can be applied together, to define the domain: $x\gt1$ and $x\ne1$. Therefore the domain is {$x|x\gt1$}.