9) (x+5)/(x+9) = (x+2)/5

Решение:

2. \[ \frac{x+5}{x+9} = \frac{x+2}{5} \]
3. 5(x + 5) = (x + 9)(x + 2)
4. 5x + 25 = x^2 + 2x + 9x + 18
5. 5x + 25 = x^2 + 11x + 18
6. 0 = x^2 + 11x - 5x + 18 - 25
7. 0 = x^2 + 6x - 7
8. x^2 + 6x - 7 = 0
9. D = b^2 - 4ac = 6^2 - 4(1)(-7) = 36 + 28 = 64
10. x1 = (-6 + \sqrt{64}) / 2 = (-6 + 8) / 2 = 2 / 2 = 1
11. x2 = (-6 - \sqrt{64}) / 2 = (-6 - 8) / 2 = -14 / 2 = -7

Ответ: x = 1, x = -7