ĐKXĐ: \(x>0\)
\(\Leftrightarrow\sqrt{x\left(x+3\right)}+2\sqrt{x+2}=2x+\sqrt{\dfrac{x^2+5x+6}{x}}\)
\(\Leftrightarrow\sqrt{x\left(x+3\right)}+2\sqrt{x+2}=2x+\sqrt{\dfrac{\left(x+2\right)\left(x+3\right)}{x}}\)
\(\Leftrightarrow\sqrt{x\left(x+3\right)}-\sqrt{\dfrac{\left(x+2\right)\left(x+3\right)}{x}}+2\sqrt{x+2}-2x=0\)
\(\Leftrightarrow\sqrt{\dfrac{x+3}{x}}\left(x-\sqrt{x+2}\right)-2\left(x-\sqrt{x+2}\right)=0\)
\(\Leftrightarrow\left(\sqrt{\dfrac{x+3}{x}}-2\right)\left(x-\sqrt{x+2}\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{\dfrac{x+3}{x}}=2\\x=\sqrt{x+2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x+3}{x}=2\\x^2=x+2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+3=2x\\\left(x+1\right)\left(x-2\right)=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=2\\x=-1< 0\left(loại\right)\end{matrix}\right.\)
