Реши уравнения: 31. x-5 / x-11 = -5, 32. 11 / x-9 = 11, 33. 10 / x-12 + 12 / x-10 = 2, 34. 12 / x-9 + 9 / x-12 = 2

31. $\frac{x-5}{x-11} = -5$ $x - 5 = -5(x - 11)$ $x - 5 = -5x + 55$ $6x = 60$ $x = 10$ **Ответ: x = 10** 32. $\frac{11}{x-9} = 11$ $11 = 11(x - 9)$ $1 = x - 9$ $x = 10$ **Ответ: x = 10** 33. $\frac{10}{x-12} + \frac{12}{x-10} = 2$ $10(x-10) + 12(x-12) = 2(x-12)(x-10)$ $10x - 100 + 12x - 144 = 2(x^2 - 22x + 120)$ $22x - 244 = 2x^2 - 44x + 240$ $2x^2 - 66x + 484 = 0$ $x^2 - 33x + 242 = 0$ $D = 33^2 - 4 \cdot 242 = 1089 - 968 = 121$ $x_1 = \frac{33 + 11}{2} = 22$ $x_2 = \frac{33 - 11}{2} = 11$ **Ответ: x = 22, x = 11** 34. $\frac{12}{x-9} + \frac{9}{x-12} = 2$ $12(x-12) + 9(x-9) = 2(x-9)(x-12)$ $12x - 144 + 9x - 81 = 2(x^2 - 21x + 108)$ $21x - 225 = 2x^2 - 42x + 216$ $2x^2 - 63x + 441 = 0$ $D = 63^2 - 4 \cdot 2 \cdot 441 = 3969 - 3528 = 441$ $x_1 = \frac{63 + 21}{4} = \frac{84}{4} = 21$ $x_2 = \frac{63 - 21}{4} = \frac{42}{4} = 10.5$ **Ответ: x = 21, x = 10.5**