Answer
The solution is
$$\lim_{x\to1^+}\left(\frac{1}{x-1}-\frac{1}{\sqrt{x-1}}\right)=\infty$$
Work Step by Step
To solve this limit follow the steps below:
$$\lim_{x\to1^+}\left(\frac{1}{x-1}-\frac{1}{\sqrt{x-1}}\right)=\lim_{x\to1^+}\left(\frac{1}{x-1}-\frac{\sqrt{x-1}}{x-1}\right)=\lim_{x\to1^+}\frac{1-\sqrt{x-1}}{x-1}=\left[\frac{1-\sqrt{1^+-1}}{1^+-1}\right]=\left[\frac{1-0^+}{0^+}\right]=\infty.$$
