Đáp án:$x = \frac{1}{2};y = \frac{5}{6};z = - \frac{5}{6}$
Giải thích các bước giải:
$\begin{array}{l}
\frac{x}{{y + z + 1}} = \frac{y}{{x + z + 2}} = \frac{z}{{x + y - 3}} = x + y + z\left( {x + y + z \ne 0} \right)\\
= \frac{{x + y + z}}{{y + z + 1 + x + z + 2 + x + y - 3}}\\
= \frac{{x + y + z}}{{2x + 2y + 2z}} = \frac{1}{2}\\
\Rightarrow \left\{ \begin{array}{l}
x + y + z = \frac{1}{2}\\
\frac{x}{{y + z + 1}} = \frac{1}{2}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
2x = y + z + 1\\
x + y + z = \frac{1}{2}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y + z = 2x - 1\\
x + 2x - 1 = \frac{1}{2}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = \frac{1}{2}\\
y = \frac{5}{6}\\
z = - \frac{5}{6}
\end{array} \right.
\end{array}$
