# What are the removable and non-removable discontinuities, if any, of f(x)=2/(x+1)?

Apr 2, 2016

There is a non-removable discontinuity when $x = - 1$.

#### Explanation:

The only discontinuity you can have with a quotient of continuous functions is when the denominator is $0$.

In your case, when $x + 1 = 0 \setminus \iff x = - 1$.

If you want to know if the discontinuity is removable, you can just compute the limit and see if it exists :

$\setminus {\lim}_{x \setminus \rightarrow - 1} f \left(x\right) = \setminus {\lim}_{x \setminus \rightarrow - 1} \frac{2}{x + 1} = \pm \infty$.

Therefore, it is not removable.