If f(x)=x+1x−2f(x) = \frac{x+1}{x-2}f(x)=x−2x+1 and g(x)=3xx+1g(x) = \frac{3x}{x+1}g(x)=x+13x, determine the domain of (f∘g)(x)(f \circ g)(x)(f∘g)(x).
R∖{−1,2}\mathbb{R} \setminus \{-1, 2\}R∖{−1,2}
R∖{−1,−23,2}\mathbb{R} \setminus \{-1, -\frac{2}{3}, 2\}R∖{−1,−32,2}
R∖{0,2}\mathbb{R} \setminus \{0, 2\}R∖{0,2}
R∖{−1,−2}\mathbb{R} \setminus \{-1, -2\}R∖{−1,−2}