ĐKXĐ: \(x\ge\frac{2}{3}\)
\(\sqrt{x+3}-\sqrt{2x-1}=\sqrt{3x-2}\)
\(\Leftrightarrow\sqrt{x+3}=\sqrt{2x-1}+\sqrt{3x-2}\)
\(\Leftrightarrow x+3=2x-1+3x-2+2\sqrt{\left(2x-1\right)\left(3x-2\right)}\)
\(\Leftrightarrow3-2x=\sqrt{\left(2x-1\right)\left(3x-2\right)}\) (\(x\le\frac{3}{2}\))
\(\Leftrightarrow\left(3-2x\right)^2=\left(2x-1\right)\left(3x-2\right)\)
\(\Leftrightarrow4x^2-12x+9=6x^2-7x+2\)
\(\Leftrightarrow2x^2+5x-7=0\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=-\frac{7}{2}< \frac{2}{3}\left(l\right)\end{matrix}\right.\)
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