Решение задачи #61934

12/(x²+2x)-3/(x²+2x-2)=1

12(x²+2x-2) - 3(x²+2x) = (x²+2x)(x²+2x-2)

x² + 2x= t

12(t-2) - 3t = t(t-2)

12t - 24 - 3t - t² + 2t = 0

t² - 11t + 24 = 0

D = 121 - 96 = 25

t₁ = (11 + 5):2 = 8

t₂ = (11 - 5):2 = 3

x² + 2x = 8

x² + 2x - 8 = 0

D = 4 + 32 = 36

x₁ = (-2 + 6):2 = 2

x₂ = (-2 - 6):2 = -4

x² + 2x = 3

x² + 2x - 3 = 0

D = 4 + 12 = 16

x₃ = (-2 + 4):2 = 1

x₄ = (-2 - 4):2 = -3

Ответ: x = 2; x = -4; x = 1; x = -3