Question

: (х+2)²/ 15х-45 ÷ х²-4/х²-6х+9 при х=4

Answer 1

Ответ:

$\frac{(x + 2 {)}^{2} }{15x - 45} \div \frac{ {x}^{2} - 4}{ {x}^{2} - 6x + 9 } = \frac{( {x} + 2 {)}^{2} }{15(x - 3)} \div \frac{(x - 2)(x + 2)}{(x - 3 {)}^{2} } = \frac{(x + 2 {)}^{2} }{15(x - 3)} \times \frac{(x - 3) {}^{2} }{(x - 2)(x + 2)} =$

Сократим (х+2)² и (х+2)

Сократим (х-3)² и (х-3)²:

$= \frac{x + 2}{15} \times \frac{x - 3}{x - 2} = \frac{(x + 2)(x - 3)}{15(x - 2)} = \frac{ {x}^{2} - 3x + 2x - 6 }{15x - 30} = \frac{ {x}^{2} - x - 6 }{15x - 30}$

х=4

$\frac{ {4}^{2} - 4 - 6 }{15 \times 4 - 30} = \frac{16 - 10}{60 - 30} = \frac{6}{30} = \frac{1}{5} = 0.2$