# Homework Help: Removable Discontinuities

1. Nov 2, 2013

### Qube

1. The problem statement, all variables and given/known data

f(x) = ln[(x-x^2)/x]

Is x = 0 a removable discontinuity?

2. Relevant equations

Removable discontinuities are points that can be filled in on a graph to make it continuous.

3. The attempt at a solution

Is it? I know that with rational functions, canceling out factors can result in removable discontinuities. For example, the function (x+2)/[(x+2)(x+3)] has a removable discontinuity at x = -2 since the factor (x+2) can be canceled out.

What about rational functions inside logarithms?

2. Nov 2, 2013

### Ray Vickson

What do you think? If you think the answer is NO, why would you think that? Ditto if you think the answer is YES.

3. Nov 2, 2013

### Simon Bridge

@Qube: you appear to have answered your own question without realizing it.
Probably you need to focus on what it means for a discontinuity to be "removeable".

... not quite right is it? If you plotted y=(x+2)/[(x+2)(x+3)] would there be a discontinuity on the graph?