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\(=\dfrac{\sqrt{x}+x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{x+\sqrt{x}+1}{\sqrt{x}+1}\)
=(căn x+1)/(căn x-1)
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\(a,C=\dfrac{2x^2-x-x-1+2-x^2}{x-1}\left(x\ne1\right)\\ C=\dfrac{x^2-2x+1}{x-1}=\dfrac{\left(x-1\right)^2}{x-1}=x-1\\ b,D=\dfrac{1+\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}\left(a>0;a\ne1\right)\\ D=\dfrac{\sqrt{a}-1}{\sqrt{a}}\)
Có
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ĐK: \(x>0;x\ne1\)
\(A=\left(\dfrac{\sqrt{x}}{\sqrt{x}+1}-\dfrac{1}{x-\sqrt{x}}\right):\left(\dfrac{1}{\sqrt{x}+1}+\dfrac{2}{x-1}\right)\)
\(=\left[\dfrac{\sqrt{x}.\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]:\left[\dfrac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\dfrac{2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]\)
\(=\dfrac{x\sqrt{x}-x-\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}:\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x\sqrt{x}-x-\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)}\)
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\(\left(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}-1}{2}\)
\(\Leftrightarrow\left[\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{x\sqrt{x}-1}-\dfrac{x+\sqrt{x}+1}{x\sqrt{x}-1}\right].\dfrac{2}{\sqrt{x}-1}\)
\(\Leftrightarrow\left[\dfrac{x+2+x-\sqrt{x}-x-\sqrt{x}-1}{x\sqrt{x}-1}\right].\dfrac{2}{\sqrt{x}-1}\)
\(\Leftrightarrow\dfrac{x+1-2\sqrt{x}}{x\sqrt{x}-1}.\dfrac{2}{\sqrt{x}-1}\)
\(\Leftrightarrow\dfrac{\left(\sqrt{x}-1\right)^2}{x\sqrt{x}-1}.\dfrac{2}{\sqrt{x}-1}\)
\(\Leftrightarrow\dfrac{\left(\sqrt{x}-1\right)2}{x+\sqrt{x}+1}\)
\(\Leftrightarrow\dfrac{2\sqrt{x}-2}{x+\sqrt{x}+1}\)
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