Answer:
-1
Step-by-step explanation:
In many cases, the simplified expression is not undefined at the point of interest.
[tex]\dfrac{\left(\dfrac{1}{\sqrt{x}}-1\right)}{\sqrt{x}-1}=\dfrac{\left(\dfrac{1-\sqrt{x}}{\sqrt{x}}\right)}{\sqrt{x}-1}=\dfrac{-1}{\sqrt{x}}[/tex]
This can be evaluated at x=1:
-1/√1 = -1
Then, the limit is ...
[tex]\boxed{\lim\limits_{x\to 1}\dfrac{\left(\dfrac{1}{\sqrt{x}}-1\right)}{\sqrt{x}-1}=-1}[/tex]
__
A graph confirms this conclusion.
