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