1) \(\left(\frac{x}{x-1}-1\right)\cdot\frac{xy-y}{xy}=\)

Область допустимых значений: \(x\ne 0\), \(x\ne 1\), \(y\ne 0\).

\(\frac{x}{x-1}-1=\frac{x-(x-1)}{x-1}=\frac{1}{x-1}\).

\(\frac{xy-y}{xy}=\frac{y(x-1)}{xy}=\frac{x-1}{x}\).

Тогда \(\frac{1}{x-1}\cdot\frac{x-1}{x}=\frac{1}{x}\).

Ответ: \(\frac{1}{x}\).