Question

Можно без решения, главное ответ.

Answer 1

8)
$( \frac{x + 3}{ {x}^{2} - 3x } + \frac{x - 3}{ {x}^{2} + 3x } ) \times \frac{9x - {x}^{3} }{ {x}^{2} + 9 } = ( \frac{x + 3}{x(x - 3)} + \frac{x - 3}{x(x + 3)} ) \times \frac{x(9 - {x}^{2} )}{ {x}^{2} + 9 } = \frac{ {(x + 3)}^{2} + {(x - 3)}^{2} }{x(x - 3)(x + 3)} \times \frac{x(3 - x)(3 + x)}{ {x}^{2} + 9} = \frac{ {x}^{2} + 6x + 9 + {x}^{2} - 6x + 9 }{x(x - 3)(x + 3)} \times \frac{ - x(x - 3)(x + 3)}{ {x}^{2} + 9} = \frac{ - (2 {x}^{2} + 18)}{ {x}^{2} + 9} = \frac{ - 2( {x}^{2} + 9)}{ {x}^{2} + 9 } = - 2$
Ответ: -2.

9)
$( {x}^{ - 1} + {y}^{ - 1} ) \times \frac{2xy}{{x}^{2} + 2xy + {y}^{2} } = ( \frac{1}{x} + \frac{1}{y} ) \times \frac{2xy}{ {(x + y)}^{2} } = \frac{y + x}{xy} \times \frac{2xy}{ {(x + y)}^{2} } = \frac{2}{x + y}$