# How do you find the x values at which #f(x)=x/(x^2-x)# is not continuous, which of the discontinuities are removable?

##### 1 Answer

A rational function is continuous on its domain and only on its domain.

#### Explanation:

The domain of

Since the solutions are

A discontinuity of function

Checking the discontinuity at

This discontinuity is removable.

Checking the discontinuity at

This discontinuity is not removable.

**Additional facts**

A discontinuity like this is sometimes called an infinite discontinuity. Infinite discontinuities are not removable.