This function g/f is not defined when the denominator 
equals 0. The denominator would equal 0 when  
which simplifies to when .  Therefore
x cannot equal 2, and 2 cannot be part of the domain
of g/f. However when , the right side 

 can be simplified to



However that cancellation cannot be made when !,
since the function is undefined there, but it can be done
for every other value of x.

So therefore we can express g/f in its simplest form 
this way:

, 

Its graph is the green graph below.  It is the horizontal
green line with a hole in it where the point (2,)
is missing and that point is NOT part of the graph of g/f:

 

So the domain of g/f is the x-axis without a value at 2.

In set-builder notation the domain of g/f would be
written .  

The graph of its domain on a number line would look just 
like the x-axis above only, shaded everywhere except at 2,
and with an open circle at 2, like this:

<========================o========>
-4  -3  -2  -1   0   1   2   3   4  

In interval notation this domain is written



Edwin