Ta có:
x-y-z=0
\(\Rightarrow\left\{{}\begin{matrix}x=y+z\\y=x-z\\z=x-y\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=y+z\\y=x-z\\-z=y-x\end{matrix}\right.\)
Thay vào A, ta có:
\(A=\left(\dfrac{x-z}{x}\right)\left(\dfrac{y-x}{y}\right)\left(\dfrac{z+y}{z}\right)\)
\(=\dfrac{y}{x}\times\dfrac{\left(-z\right)}{y}\times\dfrac{x}{z}=\dfrac{-xyz}{xyz}=-1\)