ĐK: \(\left\{{}\begin{matrix}x-2\sqrt{x}-3\ne0\\\sqrt{x}+1\ne0\\3-\sqrt{x}\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)\ne0\\\sqrt{x}+1\ne0\left(hiển-nhiên\right)\\x\ne\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow x\ne\sqrt{3}\)
\(P=\dfrac{x\sqrt{x}-3}{x-2\sqrt[]{x}-3}-\dfrac{2\left(\sqrt{x-3}\right)}{\sqrt{x}+1}+\dfrac{\sqrt{x}+3}{3-\sqrt{x}}\)
\(\Leftrightarrow\dfrac{x\sqrt{x}-3}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}-\dfrac{2\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}+\dfrac{\left(-\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}\)
\(\Leftrightarrow\dfrac{x\sqrt{x}-3-2\left(x-9\right)-x-\sqrt{x}-3\sqrt{x}-3}{\left(\sqrt{x+1}\right)\left(\sqrt{x}-3\right)}\)
\(\Leftrightarrow\dfrac{\left(x-4\right)\sqrt{x}-3x+12}{\left(\sqrt{x+1}\right)\left(\sqrt{x}-3\right)}\)
Chúc bạn học tốt ^^
