Factor the top and bottom:



Now as long as you do not cancel the (x+4)'s, then
x cannot equal to -4, because if you substitute
x = -4, you get:







That is undefined, because we cannot divide anything
by 0, not even 0 divided by 0.  It's simply undefined.
That's what causes the hole to be in the graph.

Now if we cancel the (x+4)'s we get a graph which has
no hole.





Its graph does NOT have a hole!

Notice that if we substitute x=-4 in it, we get:



So the graph goes through the point 

So the graph of



whih has no hole, is this:



That's the graph WITHOUT the hole because the point  is there, indicated by 
the darkened circle.

Now let's go back to the original equation, which has a hole,
because the (x+4)'s were not canceled:



Its graph is the same as the graph of  except
that it has a hole and doesn't go through the point . Its graph is:



So when you leave the equation as it was given originally,



And do not factor and cancel out the (x+4)'s then you have a
hole at the point that makes (x+4) equal to 0. 

Then when you factor and cancel the (x+4)'s, you "fill in" the 
hole.  There is a hole when you don't cancel, and no hole when
you do cancel.

Edwin