\(\dfrac{x+2}{3}+\dfrac{x +3}{2}+\dfrac{x+4}{1}=0\\ \Rightarrow\left\{{}\begin{matrix}\dfrac{x+2}{3}=0\\\dfrac{x+3}{2}=0\\\dfrac{x+4}{1}=0\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x+2=0\\x+3=0\\x+4=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-2\\x=-3\\x=-4\end{matrix}\right.\)