6 / (x+1) (x+2) + 8 / (x-1) (x+4) = 1

(x+1) * (x+2) = x^2 + 3x+2;

(x-1) * (x+4) = x^2+3x - 4;

x^2 + 3x = y;

(6 / (y+2)) + (8 / (y-4)) = 1;

y не=-2 и y не=4;

6 * (y-4) + 8 * (y+2) = (y+2) * (y-4) ;

6y-24 + 8y + 16 = y^2 - 2y - 8;

y^2 - y * (2+8+6) - 8 + 24 - 16 = 0;

y^2 - 16y = 0;

y * (y-16) = 0;

y=0 или y-16=0;

1) y=0; x^2+3x = 0; x * (x+3) = 0; x1=0; или x2=-3.

2) y-16 = 0; x^2+3x - 16 = 0;

D = 3^2 + 4*16 = 9+64 = 73;

x3 = (-3 + (V73)) / 2;

x4 = (-3 - (V73)) / 2.