Question

Simplify the rational expression. State any excluded values.

Answer 1

So on the top, you split it up using the difference of squares rule.
You get (x - 6)(x + 6) on the top.

On the bottom, you can undistribute (pull out) -7x.
This gives you -7x(x-6) on the bottom.

Now you can cancel like terms in the numerator and denominator.
You can cancel the (x-6).
You can also move the negative sign from the 7x to the (x + 6)

This leaves you with -(x + 6) over 7x, or (6 - x) over 7x.

To find excluded values, all you need to know is that you can't divide by zero under any circumstances, and you can't have a zero on the top in a rational expression. 
The only values for x that would make either of these statements true are if x = 0 (7 × 0 = 0 on the bottom), or if x = 6 (6 - 6 +0 on the top)

So the answer is (6 - x) over 7x, x ≠ 0, 6