Question

СРОЧНО ДАЮ 100БАЛЛОВ!!!!ДОВЕСТИ ТОТОЖНІСТЬ ​

Answer 1

$( \frac{7}{x + 7} + \frac{ {x}^{2} + 49}{ {x}^{2} - 49 } - \frac{7}{7 - x} ) \times \frac{x - 7}{ {x}^{2} + 14x + 49 } = \\ = ( \frac{7}{x + 7} + \frac{ {x}^{2} + 49}{ (x - 7)(x + 7)} + \frac{7}{x - 7} ) \times \frac{x - 7}{ (x + 7) {}^{2} } = \\ = \frac{(7(x - 7) + {x}^{2} + 49 + 7(x + 7)) }{(x + 7)(x - 7)} \times \frac{x - 7}{(x + 7) {}^{2} } = \\ = \frac{7x - 49 + {x}^{2} + 49 + 7x + 49}{(x + 7) {}^{3} } = \frac{ {x}^{2} + 14x + 49 }{(x + 7) {}^{3} } = \\ = \frac{(x + 7) {}^{2} }{(x + 7) {}^{3} } = \frac{1}{x + 7}$