ĐKXĐ : \(\left\{{}\begin{matrix}x\ge0\\x\ne0\\\sqrt{x}-1\ne0\end{matrix}\right.\) => \(\left\{{}\begin{matrix}x\ge0\\x\ne0\\x\ne1\end{matrix}\right.\) => \(\left\{{}\begin{matrix}x>0\\x\ne1\end{matrix}\right.\)
Ta có : \(P=\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{\sqrt{x}+1}{\sqrt{x}-1}\right)\left(\frac{1}{2\sqrt{x}}-\frac{\sqrt{x}}{2}\right)^2\)
=> \(P=\left(\frac{\left(\sqrt{x}-1\right)^2}{x-1}-\frac{\left(\sqrt{x}+1\right)^2}{x-1}\right)\left(\frac{1}{2\sqrt{x}}-\frac{x}{2\sqrt{x}}\right)^2\)
=> \(P=\left(\frac{\left(\sqrt{x}-1\right)^2-\left(\sqrt{x}+1\right)^2}{x-1}\right)\left(\frac{1-x}{2\sqrt{x}}\right)^2\)
=> \(P=\left(\frac{\left(\sqrt{x}-1+\sqrt{x}+1\right)\left(\sqrt{x}-1-\sqrt{x}-1\right)}{x-1}\right)\left(\frac{1-x}{2\sqrt{x}}\right)^2\)
=> \(P=\left(\frac{-4\sqrt{x}}{x-1}\right)\left(\frac{1-x}{2\sqrt{x}}\right)^2\)
=> \(P=\frac{-4\sqrt{x}\left(x-1\right)^2}{\left(2\sqrt{x}\right)^2\left(x-1\right)}\)
=> \(P=-\frac{x-1}{\sqrt{x}}\)
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