# What are the removable discontinuities of #f(x) = (x^3 - 3x^2 - x + 3) / (x+1)#?

##### 1 Answer

The only discontinuity is at

#### Explanation:

Rational functions are continuous on their domains. (They are continuous except where the denominator is zero.)

Not the when

We'll need the factoring in a minute, so either do the division or factor by grouping:

# = x^2(x-3)-1(x-3)#

# = (x^2-1)(x-3) = (x+1)(x-1)(x-3)#

# = lim_(xrarr-1)((x-1)(x-3))#

# = (-2)(-4)=8#

Because this limit exists, the discontinuity is removable.

**Not asked for, but**

To remove the discontinuity, define

Note that