Question

даю 100 балів будь ласка​

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

а)

$( \frac{x }{ {x}^{2} - 8x + 16 } - \frac{x + 6}{ {x}^{2} -1 6 } ) \div \frac{x + 12}{ {x}^{2} - 16} =\\= (\frac{x}{(x - 4) {}^{2} } - \frac{x + 6}{(x - 4)(x + 4)} ) \div \frac{(x - 4)(x + 4)}{ x+ 12} = \\ = \frac{x(x + 4) - (x + 6)(x - 4)}{(x - 4) {}^{2}(x + 4) } \times \frac{(x - 4)(x + 4)}{x + 12} = \\= \frac{ {x}^{2} + 4x - {x}^{2} + 4x - 6x + 24 }{x - 4} \times \frac{1}{x + 12} = \\ = \frac{2x + 24}{x - 4} \times \frac{1}{x + 12 } = \frac{2(x + 12)}{(x - 4)(x + 12)} = \frac{2}{x - 4}$

б)

$4 \sqrt{45} - \frac{1}{5} \sqrt{125} + \frac{1}{4} \sqrt{20} =\\= 4 \sqrt{9 \times 5} - \frac{1}{5} \sqrt{25 \times 5} + \frac{1}{4} \sqrt{4 \times 5} = \\ = 4 \sqrt{ {3}^{2} \times 5} - \frac{1}{5} \sqrt{ {5}^{2} \times 5} + \frac{1}{4} \sqrt{ {2}^{2} \times 5 } = \\= 3 \times 4 \sqrt{5} - \frac{5}{5} \sqrt{5} + \frac{2}{4} \sqrt{5} = \\ = 12 \sqrt{5} - \sqrt{5} + 0.5 \sqrt{5} = (12 - 1 + 0.5) \sqrt{5} = 11.5 \sqrt{5}$