The form (f/g)(x) is equal to f(x) divided by g(x). From the equation given by the question, the form (f/g)(x) is just equal to (2x^2+x-3) divided by (x-1).
(f/g)(x) = (2x^2+x-3)/(x-1)
(f/g)(x) = (2x+3)(x-1) / (x-1)
(f/g)(x) = (2x+3)
To get the domain, equate (2x+3) to zero.
2x+3 = 0
x = -(3/2)
So the domain is all set of integers except -(3/2)
