[tex]( \frac{x}{xy - {y}^{2} } - \frac{y}{ {x}^{2} - xy } ) \div \frac{ {x}^{2} - {y}^{2} }{8xy} = ( \frac{x}{y(x - y)} - \frac{y}{x(x - y)} ) \div \frac{(x - y)(x + y)}{8xy} = \\ \\ = ( \frac{ {x}^{2} }{xy(x - y)} - \frac{ {y}^{2} }{xy(x - y)} ) \div \frac{(x - y)(x + y)}{8xy} = \frac{ {x}^{2} - {y}^{2} }{xy(x - y)} \div \frac{(x - y)(x + y)}{8xy} = \frac{(x - y)(x + y)}{xy(x -y )} \times \frac{8xy}{(x - y)(x + y)} = \frac{8}{x - y} [/tex]