ĐKXĐ: \(x\ge1\)
\(\Leftrightarrow\left(\sqrt{2x^2+6x-8}-3\sqrt{x+3}\right)+\left(\sqrt{2x^2+4x-6}-\frac{8}{3}\sqrt{x+4}\right)+1-\frac{1}{3}\sqrt{x+4}=0\)
\(\Leftrightarrow\frac{2x^2-3x-35}{\sqrt{2x^2+6x-8}+3\sqrt{x+3}}+\frac{18x^2-28x-310}{3\left(\sqrt{2x^2+4x-6}+8\sqrt{x+4}\right)}-\frac{x-5}{3\left(\sqrt{x+4}-3\right)}=0\)
\(\Leftrightarrow\frac{\left(x-5\right)\left(2x+7\right)}{\sqrt{2x^2+6x-8}+3\sqrt{x+3}}+\frac{\left(x-5\right)\left(18x+62\right)}{3\left(\sqrt{2x^2+4x-6}+8\sqrt{x+4}\right)}-\frac{x-5}{3\left(\sqrt{x+4}+3\right)}=0\)
\(\Leftrightarrow\left(x-5\right)\left(\frac{2x+7}{\sqrt{2x^2+6x-8}+3\sqrt{x+3}}+\frac{18x+62}{3\left(\sqrt{2x^2+4x-6}+8\sqrt{x+4}\right)}-\frac{1}{3\left(\sqrt{x+4}+3\right)}\right)=0\)
\(\Leftrightarrow x=5\)
