Question

Simplify the rational expression state Any excluded values

Answer 1

Before you start realize that division by zero is undefined.  So x cannot equal 6 as 6-6=0.  With that noted, you can factor the numerator which is a difference of squares of the form (a^2-b^2) which always factors to (a+b)(a-b).  In this case the difference of squares is (x^2-36) so it is equal to (x+6)(x-6) so you have:

[(x+6)(x-6)]/(6-x)  now you can factor out -1 from the second term in the numerator to get:

[-1(x+6)(6-x)]/(6-x)  so the (6-x)s cancel out leaving:

-1(x+6) which is equal to

-x-6 which is the simplified form of the original equation.

So the answer is D. as -x-6 and x cannot equal 6.