Решить уравнение - 6/х^2-9-х+1/х-3=1/х+3

-6 / (x-3) (x+3) - (x+1) / (x-3) = 1 / (x+3)

(-6 - (x+1) (x+3)) / (x-3) (x+3) = 1 / (x+3)

(-6 - (x²+3x+x+3)) / (x-3) (x+3) = 1 / (x+3)

(-6 - x² - 4x - 3) / (x-3) (x+3) - 1 / (x+3) = 0

(-9 - x² - 4x - (x-3)) / (x-3) (x+3) = 0

-9 - x² - 4x - x + 3 = 0

-x² - 5x - 6 = 0, * (-1)

x² + 5x + 6 = 0

D = b² - 4ac

(a=1, b=5, c=6)

D = 25 - 4*6 = 1

x1, x2 = (-b+-корень изD) / 2a

x1 = (-5 - 1) / 2 = - 3

x2 = (-5 + 1) / 2 = - 2

ответ: x = - 2, x = - 3