M = (\(\frac{2x}{x\sqrt{x}+\sqrt{x}-x-1}-\frac{1}{\sqrt{x}-1}\)) : (\(1+\frac{\sqrt{x}}{x+1}\))
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3 tháng 1 2016
\(\Rightarrow C=1+\left[\frac{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\left(1-\sqrt{x}\right)\left(\sqrt{x}+1\right)}-\frac{2x\sqrt{x}-\sqrt{x}+x}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}+x\right)}\right].\frac{x-\sqrt{x}}{2\sqrt{x}-1}\)
\(=1+\left[\frac{\left(2\sqrt{x}-1\right)\left(1+\sqrt{x}+x\right)-\left(2x\sqrt{x}-\sqrt{x}+x\right)}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}+x\right)}\right].\frac{x-\sqrt{x}}{2\sqrt{x}-1}\)
\(=1+\left[\frac{2\sqrt{x}+2x+2x\sqrt{x}-1-\sqrt{x}-x-2x\sqrt{x}+\sqrt{x}-x}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}+x\right)}\right].\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{2\sqrt{x}-1}\)
\(=1+\left[\frac{2\sqrt{x}-1}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}+x\right)}\right].-\frac{\sqrt{x}\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\)
\(=1-\frac{\sqrt{x}}{1+\sqrt{x}+x}\) \(=\frac{1+\sqrt{x}+x-\sqrt{x}}{1+\sqrt{x}+x}=\frac{1+x}{1+\sqrt{x}+x}\)
1 tháng 2 2022
\(P=\dfrac{x+\sqrt{x}+1-x+\sqrt{x}-1}{\sqrt{x}}+\dfrac{x-1}{\sqrt{x}}\cdot\dfrac{x+2\sqrt{x}+1+x-2\sqrt{x}+1}{x-1}\)
\(=2+\dfrac{2x+2}{\sqrt{x}}=\dfrac{2x+2\sqrt{x}+2}{\sqrt{x}}\)
7 tháng 8 2019
\(A=\left(\frac{2x\sqrt{x}+x-\sqrt{x}}{x\sqrt{x}-1}-\frac{x+\sqrt{x}}{x-1}\right)\cdot\frac{x-1}{2x+\sqrt{x}-1}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
\(A=\left[\frac{\sqrt{x}\left(2x+\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]\cdot\frac{x-1}{2x+\sqrt{x}-1}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
\(A=\left(\frac{\sqrt{x}\left(\sqrt{x}+1\right)\left(2x+\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}-\frac{\sqrt{x}\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}\right)\cdot\frac{x-1}{2x+\sqrt{x}-1}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
\(A=\frac{\sqrt{x}\left(\sqrt{x}+1\right)\left(2x+\sqrt{x}-1-x-\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}\cdot\frac{x-1}{2x+\sqrt{x}-1}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
\(A=\frac{\sqrt{x}\left(x-2\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\frac{x-1}{2x+\sqrt{x}-1}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
\(A=\frac{\sqrt{x}\left(x-2\right)\left(\sqrt{x}+1\right)}{\left(x+\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
\(A=\frac{\sqrt{x}\left(x-2\right)}{\left(2\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\frac{\sqrt{x}\left(x+\sqrt{x}+1\right)}{\left(2\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(A=\frac{x\sqrt{x}-2\sqrt{x}+x\sqrt{x}+x+\sqrt{x}}{\left(2\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(A=\frac{2x\sqrt{x}-\sqrt{x}+x}{\left(2\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(A=\frac{\sqrt{x}\left(2x+\sqrt{x}-1\right)}{\left(2\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(A=\frac{\sqrt{x}\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\left(2\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(A=\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{x+\sqrt{x}+1}\)
\(ĐKXĐ:\hept{\begin{cases}x\ge0\\x\ne1\end{cases}}\)
\(M=\left(\frac{2x}{x\sqrt{x}+\sqrt{x}-x-1}-\frac{1}{\sqrt{x}-1}\right):\left(1+\frac{\sqrt{x}}{x+1}\right)\)
\(\Leftrightarrow M=\left(\frac{2x}{\left(x+1\right)\left(\sqrt{x}-1\right)}-\frac{1}{\sqrt{x}-1}\right):\frac{x+\sqrt{x}+1}{x+1}\)
\(\Leftrightarrow M=\frac{2x-x-1}{\left(x+1\right)\left(\sqrt{x}+1\right)}\cdot\frac{x+1}{x+\sqrt{x}+1}\)
\(\Leftrightarrow M=\frac{x-1}{\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}\)
\(\Leftrightarrow M=\frac{x-1}{x\sqrt{x}+1}\)
tự làm là hạnh phúc của mỗi công dân.