Решите уравнение:

1/x-8 - 1/x-2 = 1/x-11 - 1/x-10

X - 2 - (x - 8) / (x - 8) (x - 2) = x - 10 - (x - 11) / (x - 11) (x - 10)

x - 2 - x + 8 / (x - 8) (x - 2) = x - 10 - x + 11 / (x - 11) (x - 10)

6 / (x - 8) (x - 2) = 1 / (x - 11) (x - 10)

6 * (x - 11) (x - 10) = 1 * (x - 8) (x - 2)

6 * (x² - 10x - 11x + 110) = x² - 2x - 8x + 16

6 * (x² - 21x + 110) = x² - 10x + 16

6x² - 126x + 660 - x² + 10x - 16 = 0

5x² - 116x + 644 = 0

D = b² - 4ac = (- 116) ² - 4 * 5 * 644 = 13456 - 20 * 644 = 13456 - 12880 = 576 = 24²

x₁ = 116 + 24 / 10 = 14

x₂ = 116 - 24 / 10 = 9,2