for a ratonal, the expression only makes sense if the denominator is not 0, since if that occurs then the expression becomes undefined, a division by 0 is always undefined, for this case, when does that occur? Let's set the denominator to 0 and solve for "x".
[tex]\cfrac{\sqrt{2}}{\sqrt{x-1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{setting the denominator to 0}}{\sqrt{x-1}=0\implies (\sqrt{x-1})^2=0^2}\implies x-1=0\implies x=1[/tex]
well then, let's see what happens when x = 1
[tex]\cfrac{\sqrt{2}}{\sqrt{x-1}}\implies \cfrac{\sqrt{2(1)}}{\sqrt{1-1}}\implies \cfrac{\sqrt{2}}{\sqrt{0}}\implies \cfrac{\sqrt{2}}{0}\leftarrow und efined[/tex]
so the only values that makes sense is anything but x < 1, because a smaller value of 1 will give us an imaginary value from the root, so the only values that makes sense are namely { x | x ∈ ℝ; x > 1 }
