Найдите корни уравнения ((5x+4) / (3x^2+9x)) - ((6-7x) / (x^2-3x)) = ((3x+1) / (9-x^2))

(5x + 4) / (3x (x + 3) - (6 - 7x) / (x (x - 3) = (3x + 1) / (3 - x) (3 + x)

(5x + 4) / 3x (x + 3) + (6 - 7x) / x (3 - x) = (3x + 1) / (3 - x) (3 + x)

ОДЗ:

x ≠ 0

x≠ - 3

x≠ 3

Умножим всё уравнение на 3x (3 - x) (x + 3)

(5x + 4) (3 - x) + 3 (6 - 7x) (x + 3) = 3x (3x + 1)

15x - 5x² + 12 - 4x + 3 (6x + 18 - 7x² - 21x) = 9x² + 3x

-14x² + 8x + 12 + 3 (-7x² - 15x + 18) = 0

-14x² + 8x + 12 - 21x² - 45x + 54 = 0

-35x² - 37x + 66 = 0

35x² + 37x - 66 = 0

D = 37² + 4·66·35 = 10609 = 103²

x₁ = (-37 + 103) / 70 = 66/70 = 33/35

x₂ = (-37 - 103) / 70 = - 140/70 = - 2

Ответ: x = - 2; 33/5.