1 / (x-1) + 11 / (x-11) = 9 / (x-9) + 10 / (x-10)

1. Сгруппируем:

1 / (x - 1) + 11 / (x - 11) = 9 / (x - 9) + 10 / (x - 10); 11 / (x - 11) - 10 / (x - 10) = 9 / (x - 9) - 1 / (x - 1).

2. Приведем к общему знаменателю:

(11 (x - 10) - 10 (x - 11)) / (x - 11) (x - 10) = (9 (x - 1) - (x - 9)) / (x - 9) (x - 1); (11x - 110 - 10x + 110) / (x - 11) (x - 10) = (9x - 9 - x + 9) / (x - 9) (x - 1); x / (x - 11) (x - 10) = 8x / (x - 9) (x - 1).

1)

x1 = 0;

2)

8 / (x - 9) (x - 1) = 1 / (x - 11) (x - 10); 8 (x - 11) (x - 10) = (x - 9) (x - 1); 8x^2 - 168x + 880 = x^2 - 10x + 9; 7x^2 - 158x + 871 = 0; D/4 = 79^2 - 7 * 871 = 144; x = (79 ± √144) / 7 = (79 ± 12) / 7; x2 = (79 - 12) / 7 = 67/7; x3 = (79 + 12) / 7 = 91/7 = 13;

Ответ: 0; 67/7; 13.