Calculating Limit of Function – A difference of quotients – Exercise 5379

Exercise

Evaluate the following limit:

$$\lim _ { x \rightarrow 1} \frac{1}{x-1}-\frac{1}{\ln x}$$

$$\lim _ { x \rightarrow 1} \frac{1}{x-1}-\frac{1}{\ln x}=-\frac{1}{2}$$