What is the limit of the fraction (x^3-2x^2)/(x-2) for x-->2 ?

We notice that substituting x by 2, we'll get a
indetermination case:

lim  (x^3-2x^2)/(x-2) = (8 - 8)/(2-2)
= 0/0

We'll factorize the numerator by
x^2:

lim  (x^3-2x^2)/(x-2) = lim x^2(x -
2)/(x-2)

We'll simplify and we'll
get:

lim x^2(x - 2)/(x-2) = lim
x^2

We'll substitute x by
2:

lim x^2 =
2^2

lim  (x^3-2x^2)/(x-2) =
4