on the page http://www.purplemath.com/modules/rtnldefs2.htm#continue

Question

on the page http://www.purplemath.com/modules/rtnldefs2.htm#continue at the bottom, is the 'technically-complete answer' not actually complete? should it not say that x cannot equal -2, as well as -3?

Answer 1

Luka,

 

I looked at the page you refer to and I think I can see why you are confused.  Let's look at the problem as posed:

 

(x + 3)(x + 4)

——————

(x + 3)(x + 2)

 

On the preceding page it states that the 1st step is to find the domain of the expression.  We see here that our domain is:  x ≠ -3, x ≠ -2

 

In the simplified expression:

 

(x + 4)

———

(x + 2)

 

It would appear that domain would be x ≠ -2.  The x ≠ -3 is hidden by the act of simplification of the original expression and that is why it is being singled out and noted at this stage in the solution, to make sure that it is still included in the domain.  But you are quite correct x ≠ -2 is still certainly part of the correct domain.