ĐK: \(x\ge0;x\ne27\)
\(\left(\dfrac{x\sqrt{x}-3\sqrt{3}x}{x-27}+\dfrac{x^3-x^2+x}{3\sqrt{3}x+x\sqrt{x}}\right):\dfrac{x^2+1}{\sqrt{x}+3\sqrt{3}}=1\\ \Rightarrow\left(\dfrac{x\left(\sqrt{x}-3\sqrt{3}\right)}{\left(\sqrt{x}-3\sqrt{x}\right)\left(\sqrt{x}+3\sqrt{3}\right)}+\dfrac{x\left(x^2-x+1\right)}{x\left(\sqrt{x}+3\sqrt{3}\right)}\right):\dfrac{x^2+1}{\sqrt{x}+3\sqrt{3}}=1\\ \Rightarrow\left(\dfrac{x}{\sqrt{x}+3\sqrt{3}}+\dfrac{x^2-x+1}{\sqrt{x}+3\sqrt{3}}\right):\dfrac{x^2+1}{\sqrt{x}+3\sqrt{3}}=1\\ \Rightarrow\dfrac{x^2+1}{\sqrt{x}+3\sqrt{3}}:\dfrac{x^2+1}{\sqrt{x}+3\sqrt{3}}=1\\ \Rightarrow1=1\)
Ta có điều cần chứng minh.
