What Is the Limit of (2-x)/(x^2-4) as x Approaches 2?

[screamtrumpet]

lim (2-x)/(x^2-4)
x>2

Find the limit(is it exists)

The substitution method failed so I factored the bottomto (x+2)(x-2).Where do I go from here?

 

[HallsofIvy]

A very important but often overlooked "law of limits":

If f(x)= g(x) for all x except x= a, then \displaytype\lim_{x\to a}f(x)= \lim_{x\to a} g(x).

Here, for all x except x= 2, (2- x)/(x-2)(x+2)= -1/(x+2).

 

[Oerg]

use l'Hospital's rule

 

[screamtrumpet]

Thank you