# What are the removable and non-removable discontinuities, if any, of #f(x)=(x^4+4x^2+2x)/(x^2-2x)#?

##### 1 Answer

There is a removable discontinuity at

#### Explanation:

Therefore,

The domain of

So

In order to determine whether a discontinuity is removable, we need to look at the limit of

**At #x=0#**

This limit has indeterminate form

# = lim_(xrarr0)(x^3+4x+2)/(x-2) = -1#

Because the limit exists, the discontinuity is removable.

**At #x=2#**

This limit has form