Đáp án:Tham khảo
Giải thích các bước giải:
$\text{ĐK}$:\(\left[ \begin{array}{l}:x-1\neq 0\\3x-1\neq 0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x\neq 1\\x\neq \dfrac{1}{3}\end{array} \right.\)
$\text{Ta có:}$
$(x³-1):(x-1)-(9x²-1):(3x-1)=0$
$⇔(x-1)(x²+x+1):(x-1)-[(3x)²-1²]:(3x-1)=0$
$⇔(x-1)(x²+x+1):(x-1)-(3x-1)(3x+1):(3x-1)=0$
$⇔(x²+x+1)-(3x+1)=0$
$⇔x²+x+1-3x-1=0$
$⇔x²-2x=0$
$⇔x(x-2)=0$
⇔\(\left[ \begin{array}{l}x=0\\x-2=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x=2\end{array} \right.\)
$\text{Vậy x∈(0;2)}$
