Find the limit of the following described function (it's hard to format it correctly) as x-->2

Question

The function is a fraction. Within the numerator there is another fraction: (x+2)/x. And this fraction has 2 subtracted it from it. The denominator of the function is simply x-2. 

Is the limit defined?

Answer 1

We can multiply the numerator and denominator by x to get

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

Therefore, the limit as x approaches 2 is -1/2.