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