$\dfrac{1}{x+1}+\dfrac{2x^2+1}{x^3+1}+\dfrac{2x^3-2x^2}{x^2-x+1}=2x$
$↔\dfrac{x^2-x+1+2x^2+1+(2x^3-2x^2)(x+1)}{(x+1)(x^2-x+1)}=\dfrac{2x(x^3+1)}{(x+1)(x^2-x+1)}$
$↔3x^2+2-x+2x^2(x+1)(x-1)=2x^4+2x$
$↔3x^2-x+2+2x^4-2x^2-2x^4-2x=0$
$↔x²-3x+2=0$
$↔(x-1)(x-2)=0$
\(\leftrightarrow\left[ \begin{array}{l}x-1=0\\x-2=0\end{array} \right.\) \(\leftrightarrow\left[ \begin{array}{l}x=1\\x=2\end{array} \right.\)
Vậy pt có tập nghiệm $S=\{1;2\}$
