ĐKXĐ: x>1; x<>10
\(P=\left(\dfrac{\sqrt{x-1}}{3+\sqrt[]{x-1}}+\dfrac{x+8}{10-x}\right):\left(\dfrac{3\sqrt{x-1}+1}{x-3\sqrt{x-1}-1}-\dfrac{1}{\sqrt{x-1}}\right)\)
\(=\left(\dfrac{\sqrt{x-1}\left(\sqrt{x-1}-3\right)}{\left(\sqrt{x-1}+3\right)\left(\sqrt{x-1}-3\right)}-\dfrac{x+8}{\left(\sqrt{x-1}-3\right)\left(\sqrt{x-1}+3\right)}\right):\left(\dfrac{3\sqrt{x-1}+1}{\sqrt{x-1}\cdot\left(\sqrt{x-1}-3\right)}-\dfrac{1}{\sqrt{x-1}}\right)\)
\(=\dfrac{x-1-3\sqrt{x-1}-x-8}{\left(\sqrt{x-1}+3\right)\left(\sqrt{x-1}-3\right)}:\dfrac{3\sqrt{x-1}+1-\sqrt{x-1}+3}{\sqrt[]{x-1}\left(\sqrt{x-1}-3\right)}\)
\(=\dfrac{-3\sqrt{x-1}-9}{\left(\sqrt{x+1}+3\right)\left(\sqrt{x-1}-3\right)}\cdot\dfrac{\sqrt{x-1}\left(\sqrt{x-1}-3\right)}{2\sqrt{x-1}+4}\)
\(=\dfrac{-3\left(\sqrt{x-1}+3\right)}{\left(\sqrt{x+1}+3\right)}\cdot\dfrac{\sqrt{x-1}}{2\sqrt{x-1}+4}=\dfrac{-3\sqrt{x-1}}{2\sqrt{x-1}+4}\)
