Why is x-2 / x+2 not equal to -1?

The value of the expression (x - 2)/(x + 2) depends upon the value of the variable x.

(x - 2)/(x + 2) equals -1 only when x is zero.

If x represents any number other than 0, then (x - 2)/(x + 2) does not equal -1.

If x represents the number -2, then the expression (x - 2)/(x + 2) does not equal anything; it's "undefined".
 
For a quotient to be -1, the numerator and denominator must be opposites of each other.
The opposite of x + 2 is not x - 2. The opposite of x + 2 is -x - 2.
The opposite of x - 2 is not x + 2. The opposite of x - 2 is -x + 2, or 2 - x.
 
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