Question

How do you evaluate the limit `(2-x)/(x^2-4)` as x approaches `2`?

Answer 1

Factor and reduce.

Explanation:

We'll need to know `a-b = -(b-a)`.

Factor and simplify:

`(2-x)/(x^2-4) = (2-x)/((x-2)(x+2))`

`= (-(x-2))/((x-2)(x+2))`

`= (-1)/(x+2)`.

So the limit is `-1/4`