Question

What is the domain and range of 2x^2-18/x^2+3x-10

Answer 1

for rational functions, y = p(x)/q(x), the domain is all reals except where q(x) = 0

So, here that would be all reals except where (x+5)(x-2) = 0

since there is a horizontal asymptote at y=2, and the graph does not cfross the asymptote, the range would be all reals except y=2

y = 2 + (2-6x)/(x^2+3x-10)

Answer 2

The way you typed it, we are only dividing by x^2 ,so the domain is any real number, except x = 0

If you meant:
(2x^2 - 18)/(x^2 + 3x - 10)
= 2(x-3)(x+3)/( (x+5)(x-2) )

the domain is any real number , x ≠ 2 , -5