Put \(x-y=a\)

\(\Rightarrow\dfrac{x-y+y-z}{y-z}=\dfrac{a+\left(y-z\right)}{y-z}=\dfrac{a}{y-z}+\dfrac{y-z}{y-z}=\dfrac{x-y}{y-z}+1\)

But \(\dfrac{x-y}{z-y}+\dfrac{x-y}{y-z}=0\)

\(\Rightarrow\dfrac{x-y}{y-z}+1=2+1=3\)

\(\dfrac{x-y}{z-y}=-2\Rightarrow x-y=2\left(y-z\right)\Rightarrow x-y=2y+z-3z\)

\(\Rightarrow x-z=2y-3z+y\Rightarrow x-z=3\left(y-z\right)\Rightarrow\dfrac{x-z}{y-z}=3\)