ĐK :$x>\frac{2}{3}$
pt$\Leftrightarrow \frac{x^2}{3x-2}-1+x-\sqrt{3x-2} =0$
$\Leftrightarrow \frac{x^2-(3x-2)}{3x-2}+x-\sqrt{3x-2} =0$
$\Leftrightarrow \frac{(x-\sqrt{3x-2})(x+\sqrt{3x-2})}{3x-2}+(x-\sqrt{3x-2})=0$
$\Leftrightarrow (x-\sqrt{3x-2})(\frac{x+\sqrt{3x-2}}{3x-2}+1)=0$
$\Leftrightarrow \left[\begin{matrix} x=\sqrt{3x-2}(*)\\ \frac{x+\sqrt{3x-2}}{3x-2}+1=0 (**) \end{matrix} {} \right.$
+) Ta có (*)$\Leftrightarrow x^2-3x+2=0\Leftrightarrow \left[ \begin{matrix} x=1\\ x=2 \end{matrix}{} \right.$(thỏa mãn ĐK)
+) (**) vô nghiệm do $x>2/3$
Vậy pt có 2 nghiệm