(2x^2-x-6)/x^2-4
Factor top and bottom and you get
(2x+3)(x-2)/(x+2)(x-2)
The (x-2) cancel out each other leaving,
(2x+3)/x+2
The domain is all real numbers EXCEPT for -2. The domain can never be -2 as it would to the bottom having a zero, and that can't happen