ĐKXĐ: \(\dfrac{3}{2}\le x\le6\)
\(\sqrt{2x-3}-\sqrt{6-x}=-1\)
\(\Leftrightarrow\sqrt{2x-3}-1+2-\sqrt{6-x}=0\)
\(\Leftrightarrow\dfrac{\left(\sqrt{2x-3}-1\right)\left(\sqrt{2x-3}+1\right)}{\sqrt{2x-3}+1}+\dfrac{\left(2-\sqrt{6-x}\right)\left(2+\sqrt{6-x}\right)}{2+\sqrt{6-x}}=0\)
\(\Leftrightarrow\dfrac{2\left(x-2\right)}{\sqrt{2x-3}+1}+\dfrac{x-2}{2+\sqrt{6-x}}=0\)
\(\Leftrightarrow\left(x-2\right)\left(\dfrac{2}{\sqrt{2x-3}+1}+\dfrac{1}{2+\sqrt{6-x}}\right)=0\)
\(\Leftrightarrow x-2=0\) (do \(\dfrac{2}{\sqrt{2x-3}+1}+\dfrac{1}{2+\sqrt{6-x}}>0\))
\(\Leftrightarrow x=2\)
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