Question

What is the limit of (2-x)/(x^2-4) as x approaches 2?

Answer 1

-1/4
See if you agree with the work in the attached file.

Answer 2

http://www.wolframalpha.com/input/?i=limit+as+x+approach+2+of++%28%282-x%29%2F%28x%5E2-4%29%29

Answer 3

Is one allowed to factor out a (-1) like that?

Answer 4

Yes. The -1 was factored out of the numerator only.
I learned this as the "three signs of a fraction."
Example: -(1/2) = (-1)/2 = 1/(-2)
Note: -(1/2) is never equal to (-1)/(-2) {which would be positive 1/2}

Answer 5

Thank you very much!