Answer:
[tex]\large\boxed{x\in\mathbb{R}-\{1\}}\to\text{any real number except 1}[/tex]
Step-by-step explanation:
[tex]\dfrac{x-1}{x-1}=1\\\\\text{Domain:}\ x-1\neq0\qquad\text{add 1 to both sides}\\\\x\neq1\\\\\text{We know:}\ \dfrac{a}{a}=1\ \text{for any real number except 0}.\\\\\text{Therefore}\ x\ \text{is any real number except 1}.[/tex]
