$\begin{array}{l}\text { Given } \frac{x}{y+z}=\frac{y}{z+x}=\frac{z}{x+y} \\ =k \text {. Find the value of } k \text { . }\end{array}$
Correct answer: When $x+y+z \neq 0$, we get $k=\frac{1}{2}$; when $x+y+z=0$, by substituting $y+z=-x$ into $\frac{x}{y+z}=k$, we get $k=-1$.