Simplify the rational expression. state any excluded values. x^2-36/6-x

Before you start notice that division by zero is undefined, thus the denominator cannot equal zero which means that:

6-x!=0

6!=x

So x cannot equal 6...the proceed to simplifying...

(x^2-36)/(6-x)  the numerator is a "difference of squares" having the form:

(a^2-b^2) which always factors to (a+b)(a-b) so what you actually have is:

((x+6)(x-6))/(6-x)  if you factor out -1 from the second factor in the numerator you have:

(-1(x+6)(6-x))/(6-x)  now you can see that the (6-x)s cancel out leaving:

-1(x+6) which is equal to

-x-6, just remember that x cannot equal 6 as we saw in the beginning...