Reflect right triangle ABC across line BC. Classify triangle ACA' according to its side lengths. Explain how you know.

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...