Đáp án + Giải thích các bước giải:
`(1)/(x-1)+(2)/(x^{2}+x+1)=(3x^{2})/(x^{3}-1)` `(ĐKXĐ:x\ne1)`
`⇔(x^{2}+x+1)/((x-1)(x^{2}+x+1))+(2(x-1))/((x-1)(x^{2}+x+1))=(3x^{2})/((x-1)(x^{2}+x+1))`
`⇒x^{2}+x+1+2(x-1)=3x^{2}`
`⇔x^{2}+x+1+2x-2-3x^{2}=0`
`⇔-2x^{2}+3x-1=0`
`⇔(-2x^{2}+2x)+(x-1)=0`
`⇔-2x(x-1)+(x-1)=0`
`⇔(x-1)(-2x+1)=0`
`⇔` \(\left[ \begin{array}{l}x-1=0\\-2x+1=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=1\\-2x=-1\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=1(KTM)\\x=\frac{1}{2}(TM)\end{array} \right.\)
Vậy `S={(1)/(2)}`
