problem with evaluating limit

[cotfw]

I can't figure out a problem in my calculus book:

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


Inputting 2 as x results in, 0/0, so I thought I was supposed to factor the expression to "plug in" the hole. But my factoring doesn't result in anything that seems to work.

I factored it to (x - (4/x)) / (x - 2) but that didn't work. Then I multiplied numerator and denominator by the conjugate of x-2 but that didn't work. (x^2 - 4 - 2x + 8/x) / (x^2 - 4). Do you know what I do?

 

[stapel]

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

The numerator is a difference of squares. The terms in the denominator have a common factor. Factor, top and bottom. Cancel the duplicate factor. Evaluate the result.

 

[cotfw]

The numerator is a difference of squares. The terms in the denominator have a common factor. Factor, top and bottom. Cancel the duplicate factor. Evaluate the result.

Ah I see. Thanks a lot for the help