Решите уравнение 4 / (x-9) + 9 / (x-4) = 2

ОДЗ

x ≠ 9; x ≠ 4

4 (x - 4) + 9 (x - 9) = 2 (x - 4) (x - 9)

4x - 16 + 9x - 81 = 2 (x^2 - 13x + 36)

13x - 97 = 2x^2 - 26x + 72

2x^2 - 26x + 72 - 13x + 97 = 0

2x^2 - 39x + 169 = 0

D = 169 = 13^2

x1 = (39 + 13) / 4 = 13

x2 = (39 - 13) / 4 = 6,5

Ответ

6,5; 13