x+1/x^2+x+1 - x-1/x^2-x+1 = 3/x(x^4+x^2+1) (ĐKXĐ : x khác 0 )
<=> x + 1/x^2 + x + 1 - x - 1/ x^2 - x + 1- 3/x(x^4+x^2+1) = 0
<=> x + 1/x^2 + x + 1 - x - 1/ x^2 - x + 1- 3/ x( x^4 - x^3 + x^3 +x^2 - x^2 + x - x +1) = 0
<=> x + 1/x^2 + x + 1 - x - 1/ x^2 - x + 1- 3/ x [ x^2 ( x^2 - x + 1) + x ( x^2 - x + 1) + x^2 - x +1 ] = 0
<=> x + 1/x^2 + x + 1 - x - 1/ x^2 - x + 1- 3/ x( x^2 - x + 1).(x^2 - x+ 1) =0
<=> x( x^2 - x + 1).(x + 1) - x.(x^2 + x + 1).( x - 1) - 3/ x( x^2 - x + 1)(x^2 + x + 1) = 0
<=> x(x^3 + 1) - x(x^3 - 1) -3/ x( x^2 - x + 1)(x^2 + x + 1) = 0
<=> x^4 + x - x^4 + x - 3/ x( x^2 - x + 1)(x^2 + x + 1) = 0
<=> 2x - 3/ x( x^2 - x + 1)(x^2 + x + 1) = 0
<=> 2x - 3 = 0
<=> 2x = 3
<=> x = 3/2 ( TM)
Vậy x = 3/2