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Решите задачу:

$( \frac{x + \sqrt{ {x}^{2} - 2x } }{x - \sqrt{ {x}^{2} - 2x } } - \frac{x - \sqrt{ {x}^{2} - 2x} }{x + \sqrt{ {x}^{2} - 2x} } ) \times \sqrt{ \frac{x}{ {x}^{2} - 4} } = \frac{ {(x + { \sqrt{ {x}^{2} - 2x })}}^{2} - {(x - \sqrt{ {x}^{2} - 2x }) }^{2} }{(x - \sqrt{ {x}^{2} - 2x})(x + \sqrt{ {x}^{2} + 2x} ) } \times \sqrt{ \frac{x}{ {x}^{2} - 4} } = \frac{ {x}^{2} + 2x \sqrt{ {x}^{2} - 2x} + {x}^{2} - 2x - ( {x}^{2} - 2x \sqrt{ {x}^{2} - 2x } + {x}^{2} - 2x)}{ {x}^{2} - ( {x}^{2} - 2x) } \times \sqrt{ \frac{x}{ {x}^{2} - 4} } = \frac{4x \sqrt{ {x}^{2} - 2x} }{ 2x} \times \frac{ \sqrt{ x} }{ \sqrt{ {x}^{2} - 4} } = \frac{2 \sqrt{x} \sqrt{x(x - 2)} }{ \sqrt{(x - 2)(x + 2)} } = \frac{2x}{ \sqrt{x + 2} } = \frac{2 \times 0.25}{ \sqrt{0.25 + 2} } = \frac{0.5}{ \sqrt{2.25} } = \frac{0.5}{1.5} = \frac{1}{3}$