R(x)= -7-6x/x^3-5x^2+6x submitted, I am going to assume you meant
R(x)= (-7-6x)/(x³-5x²+6x)=-(7+6x)/(x(x²-5x+6)=-(7+6x)/(x(x-3)(x-2))
The function is definable except where x=0 or 2 or 3.
The domain D is the complement, in the real line, of these points.
D=(-∞,0)∪(0,2)υ(2,3)∪(3,∞)
Comments
x cannot equal 3 and x cannot equal 2 and x cannot equal 0
is clearly correct, however your description should be the domain is (-∞,0)∪(0,2)∪(2,3)∪(3,∞), the parentheses indicating that the intervals do not contain their end points