What are the removable and non-removable discontinuities, if any, of #f(x)=2/(x+1)#?
There is a non-removable discontinuity when
The only discontinuity you can have with a quotient of continuous functions is when the denominator is
In your case, when
If you want to know if the discontinuity is removable, you can just compute the limit and see if it exists :
Therefore, it is not removable.