Question 142513
I knew this one was coming, or one like it!!  In this case, you cannot divide by zero, so x must NOT be allowed to equal -6.  Now, having said that, if you reduce the fraction, you get:
{{{f(x) = (x^2-36)/(x+6) }}} 
{{{f(x) = ((x-6)(x+6))/(x+6)}}} which reduces to {{{f(x) = (x-6) }}}, but x MUST NOT EQUAL -6!


The comment above that x cannot equal -6 is very important!!  This essentially places a HOLE in the graph!!  The graph is a straight line with a hole in it.  If you use a graphing calculator, you will see a straight line, but the hole in the graph will not show up, unless you know to look for it.  Even then, you probably won't be able to see it.  


{{{graph(300,600, -10,10,-20,20, (x^2-36)/(x+6) )}}} but there is a HOLE in the graph at x=-6!


Probably your next question will be {{{f(x) = (x+6)/(x^2-36) }}}.  This graph has an asyptote at x=6 and a hole in the graph at x=-6.  


R^2