$$(\frac{1}{y}-\frac{1}{x})(\frac{xy}{y-x})$$
$-1$
$$\left(\frac{x}{xy}-\frac{y}{xy}\right)\times \frac{xy}{y-x}$$
$$\frac{x-y}{xy}\times \frac{xy}{y-x}$$
$$\frac{\left(x-y\right)xy}{xy\left(y-x\right)}$$
$$\frac{-xy\left(-x+y\right)}{xy\left(-x+y\right)}$$
$$-1$$
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