smc

Multiply the expression by $\frac{xy}{xy}$ to get rid of the fractional numerator and denominator: $\frac{x^{2}y-x}{x{y}^2-y}$. This can be factored as $\frac{x(xy-1)}{y(xy-1)}$. The $xy-1$ terms cancel out, leaving $\frac{x}{y},\boxed{\frac{x}{y}}$.