(x²-x+1)/(x-1) +(x²+x+6)/(x+1) =8 ;
* * * ОДЗ : x≠ ± 1 * * *
(x²-x)/(x-1) +1/(x-1) + (x²+x)/(x+1)+6/(x+1) =8 ;
x(x-1)/(x-1)+ x(x+1)/(x+1) + 1/(x-1)+6/(x+1) =8 ;
2x + (x+1+6(x -1) ) / (x+1)(x-1) =8 ;
2x + (7x -5)/(x²-1) =8 ;
2x(x²-1) + (7x -5) =8(x²-1) ;
2x³ -8x² +5x +3 =0 ;
* * * x=3 корень , (2x³ -8x² +5x +3) / (x-3) * * *
2x³ - 6x² -2x² +6x -x +3 =0 ; * * * или по схеме Горнера * * *
2x²(x-3) -2x(x-3) -(x-3) =0 ;
(x-3)(2x² -2x -1) =0⇔[ x-3 =0 ; 2x² -2x -1 =0.
[x =3 ; x =(1±√3)/2.
ответ: (1-√3)/2 ; (1+√3)/2 ; 3.