In this Example 3, wouldn’t the “X does not equal” value be 4 and -4?

As in Example 2, the “X does not equal” value is 4 and -4. I think that in example 3 also, it would be 4 and -4. Correct me if I am wrong.

No; x^2 - 8x + 16 = (x - 4)^2.

That is correct. Notice though that the denominator in Example 3 and 3 aren’t the same.