Simplify by cancelling common factors from numerator and denominator.
(x² -x -6)/(x² -4) = (x -3)(x +2)/((x -2)(x +2))
= (x -3)/(x -2)
The restriction x > 2 ensures the denominator will not be zero.
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This could be written as
.. 1 -1/(x -2)
so that you can see it is a reflection of 1/x across the x-axis and a translation 1 unit up and 2 units to the right.