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...