\(\dfrac{x}{y+z+1}=\dfrac{y}{x+z+3}=\dfrac{z}{y+x-4}=x+y+z\)
\(\Rightarrow\dfrac{x}{y+z+1}=\dfrac{y}{x+z+3}=\dfrac{z}{y+x-4}=\dfrac{x+y+z}{2x+2y+2z}=\dfrac{1}{2}\)
\(\Leftrightarrow x+y+z=\dfrac{1}{2}\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{y+z+1}=\dfrac{1}{2}\\\dfrac{y}{x+z+3}=\dfrac{1}{2}\\\dfrac{z}{y+x-4}=\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=y+z+1\\2y=x+z+3\\2z=y+x-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=x+y+z+1=\dfrac{1}{2}+1=\dfrac{3}{2}\\y=x+y+z+3=\dfrac{1}{2}+3=\dfrac{7}{2}\\z=x+y+z-4=\dfrac{1}{2}-4=-\dfrac{7}{2}\end{matrix}\right.\)
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