As you have not specified what x is tending to, I take it as 2.

We have to find the value of lim x--> 2 [(x^2-3x+2)/(x^2-4)]

If we substitute x = 2, we get the indeterminate form 0/0. So we use L'Hopital's Rule and substitute the numerator and the denominator by their derivatives

=> lim x-->2 [(2x -3)/(2x)]

substitute x = 2

=> (4 - 3) / 4

=> 1/4

**The required value of lim x--> 2 [(x^2-3x+2)/(x^2-4)] =
(1/4)**

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