Find the domain for the function

Question

f(x)=-2x^(2)÷-x^(2)-6x-27

Answer 1

I will assume you meant
f(x) = -2x^2 /(-x^2 - 6x - 27)
= 2x^2/(x^2 + 6x + 27)

Are you sure you typed the signs correctly?
It would be nice if the -27 had been +27, or the - in front of x^2 would not be there.

If it is correct,
since x^2 + 6x + 27 = 0 has no real roots, the domain would be the set of all real numbers.

if you meant:
f(x)= (-2x^(2)÷-x^(2))-6x-27 , then the domain is the set of real numbers except x ≠ 0