Question

If f(x) = 2x^2-x-6 and g(x) = x^2-4 , what is the domain of f(x) divided by g(x)

Answer 1

(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