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\(\left(\frac{3\sqrt{x}\left(\sqrt{x}-3\right)+\sqrt{x}\left(\sqrt{x}+3\right)-3x-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right).\frac{\sqrt{x}-3}{2\sqrt{x}-2-\sqrt{x}+3}\)
\(\frac{3x-9\sqrt{x}+x+3\sqrt{x}-3x-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\frac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(\frac{x-6\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+1\right)}\)
voi dk \(x\ge0\) ; \(x\ne9\) ;\(x\ne1\)
Trả lời:
a, \(P=\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}-\frac{\sqrt{x}-1}{\sqrt{x}+1}\right):\left(\frac{1}{\sqrt{x}+1}-\frac{\sqrt{x}}{1-\sqrt{x}}+\frac{2}{x-1}\right)\) \(\left(ĐK:x\ge0;x\ne1\right)\)
\(=\left[\frac{\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\frac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right]:\left(\frac{1}{\sqrt{x}+1}+\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{2}{x-1}\right)\)
\(=\left[\frac{\left(\sqrt{x}+1\right)^2-\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]:\left[\frac{\sqrt{x}-1}{x-1}+\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{x-1}+\frac{2}{x-1}\right]\)
\(=\frac{x+2\sqrt{x}+1-\left(x-2\sqrt{x}+1\right)}{x-1}:\frac{\sqrt{x}-1-\sqrt{x}\left(\sqrt{x}+1\right)+2}{x-1}\)
\(=\frac{x+2\sqrt{x}+1-x+2\sqrt{x}-1}{x-1}:\frac{\sqrt{x}-1-x-\sqrt{x}+2}{x-1}\)
\(=\frac{4\sqrt{x}}{x-1}:\frac{1-x}{x-1}=\frac{4\sqrt{x}}{x-1}\cdot\frac{x-1}{1-x}=\frac{4\sqrt{x}}{1-x}\)
ĐK : \(\hept{\begin{cases}x\ge0\\x\ne9\end{cases}}\)
\(P=\left[\frac{2\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}+\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\frac{3x+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right]\cdot\frac{2\left(\sqrt{x}-1\right)}{\sqrt{x}-3}\)
\(=\frac{2x-6\sqrt{x}+x-3\sqrt{x}-3x-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\cdot\frac{2\left(\sqrt{x}-1\right)}{\sqrt{x}-3}\)
\(=\frac{-6\left(3\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-3\right)^2\left(\sqrt{x}+3\right)}\)( hơi xấu nhỉ :V )