# Let #f(x)=(x^3 - 4x)/(x^3 +x^2-6x)#, how do you find all points of discontinuity of f(x)?

##### 2 Answers

Factor the numerator and denominator to identify their zeros to determine the points of discontinuity and their types.

#### Explanation:

with exclusions

There are removable discontinuities at

There is a simple pole at

Apart from these discontinuities,

graph{(x+2)/(x+3) [-10, 10, -5, 5]}

That function has discontinuities at 0, 2, and -3.

#### Explanation:

A rational function is continuous on its domain.

So the points of discontinuity for a rational function are the point outside the domain.

The points outside the domain are:

**Note**

Because this was posted in the topic "Classifying Discontinuities, I should probably add that

So the only infinite limit occurs at

The discontinuities at