ĐKXĐ: \(-\dfrac{1}{3}< =x< =2\)
\(2x+\sqrt{3x+1}=2+2\sqrt{2-x}\)
=>\(2x-2+\sqrt{3x+1}-2-2\sqrt{2-x}+2=0\)
=>\(2\left(x-1\right)+\dfrac{3x+1-4}{\sqrt{3x+1}+2}-2\left(\sqrt{2-x}-1\right)=0\)
=>\(2\left(x-1\right)+\dfrac{3\left(x-1\right)}{\sqrt{3x+1}+2}-2\cdot\dfrac{2-x-1}{\sqrt{2-x}+1}=0\)
=>\(2\cdot\left(x-1\right)+\dfrac{3\left(x-1\right)}{\sqrt{3x+1}+2}+\dfrac{2\left(x-1\right)}{\sqrt{2-x}+1}=0\)
=>\(\left(x-1\right)\left(2+\dfrac{3}{\sqrt{3x+1}+2}+\dfrac{2}{\sqrt{2-x}+1}\right)=0\)
=>x-1=0
=>x=1(nhận)
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