To solve this equation, we first need to factor both the numerator and the denominator.

Numerator: x^2 - 3x + 2 can be factored as (x - 1)(x - 2)
Denominator: x^2 - 4 can be factored as (x + 2)(x - 2)

Therefore, the equation becomes:

(x - 1)(x - 2) / (x + 2)(x - 2) = 0

Now, we can simplify this by cancelling out the common factor of (x - 2) in the numerator and denominator:

(x - 1) / (x + 2) = 0

To find the values of x that satisfy this equation, we set the numerator equal to zero:

x - 1 = 0
x = 1

Therefore, the solution to the equation x^2 - 3x + 2 / x^2 - 4 = 0 is x = 1.