Let there is a function

f(x) = (x² - 4)/(x-2)  ;  x ≠ 2

Now this function is defined for all values of x except 2.

Let x = 2

So   f(2) = (2² - 4)/(2-2)

=> f(2) = (4-4)/0

=> f(2) = 0/0 ..............1

Again if x ≠ 2

      f(x) = (x² - 4)/(x-2)

=> f(x) = {(x - 2)*(x+2)}/(x-2)

=> f(x) = x+2

Now 

  x   :    1.4   1.5  1.6   1.7   1.8   1.9       2     2.01   2.1   2.2  2.3   2.4       

f(x) :    3.4   3.5   3.6   3.7   3.8   3.9    0/0    4.01   4.1   4.2  4.3   4.4

From the above table, we observe that

1. When x increses and colser to 2 from left hand side of 2, The value of f(x) increses and closer to 4.

2. When x decreases and colser to 2 from right hand side of 2, The value of f(x) decsrese and closer to 4.

2. When x = 2, the value of f(x) is 0/0 i.e. not defined.

So f(x) is defined at the neighbour of 2, that is why x approaches to 2 not equal to 2.