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P xác định khi \(\hept{\begin{cases}x>0\\x\ne1\end{cases}}\)

\(P=\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\frac{1}{\sqrt{x}+1}+\frac{2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\)

\(=\left(\frac{x}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\frac{\sqrt{x}-1+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\)

\(=\left(\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\frac{\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\)

\(=\frac{\sqrt{x}+1}{\sqrt{x}}:\frac{1}{\sqrt{x}-1}\)

\(=\frac{\sqrt{x}+1}{\sqrt{x}}.\left(\sqrt{x}-1\right)\)

\(=\frac{x-1}{\sqrt{x}}\)

P xác định khi \(\hept{\begin{cases}x>0\\x\ne1\end{cases}}\)

\(P=\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\frac{1}{\sqrt{x}+1}+\frac{2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\)

\(=\left(\frac{x}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\frac{\sqrt{x}-1+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\)

\(=\left(\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\frac{\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\)

\(=\frac{\sqrt{x}+1}{\sqrt{x}}:\frac{1}{\sqrt{x}-1}\)

\(=\frac{\sqrt{x}+1}{\sqrt{x}}.\left(\sqrt{x}-1\right)\)

\(=\frac{x-1}{\sqrt{x}}\)

14 tháng 12 2017

a) ĐKXĐ : \(\hept{\begin{cases}x\ge0\\\sqrt{x}-1\ne0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ge0\\x\ne1\end{cases}}\)

23 tháng 9 2018

a) DK de P xác dinh : \(\hept{\begin{cases}x\ge0\\x\ne1\end{cases}}\)

b) \(P=\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{1-x}+\frac{\left(\sqrt{x}-2\right)^2+3\sqrt{x}-x}{1-\sqrt{x}}\)

\(=\frac{\sqrt{x}}{1-\sqrt{x}}+\frac{-\sqrt{x}+4}{1-\sqrt{x}}\)

\(=\frac{4}{1-\sqrt{x}}\)

c) de P > o thì \(1-\sqrt{x}>0\Rightarrow\sqrt{x}< 1\Rightarrow0< x< 1\)

ĐKXĐ: \(x>0;x\ne1;x\ne9\)

\(B=\left(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}-3}-\frac{\sqrt{x}+3}{\sqrt{x}-1}\right)\)

\(=\frac{\sqrt{x}-\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}:\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-1\right)}\)

\(=\frac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}.\frac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-1\right)}{x-1-x+3}\)

\(=\frac{1}{\sqrt{x}}.\frac{\sqrt{x}-3}{2}\)

\(=\frac{\sqrt{x}-3}{2\sqrt{x}}\)

Để B < 0 thì 

\(\frac{\sqrt{x}-3}{2\sqrt{x}}< 0\) 

\(\Rightarrow\)\(\sqrt{x}-3\)và \(2\sqrt{x}\)trái dấu mà 

\(2\sqrt{x}\ge0\)\(\Rightarrow\sqrt{x}-3< 0\)

\(\Rightarrow\sqrt{x}< 3\)

\(\Rightarrow x< 9\)

13 tháng 8 2016

tách mẫu sau đó đối dau là ra mà .

2 tháng 9 2018

a,

\(A\Leftrightarrow\)\(\left(\frac{1}{\sqrt{x}-1}-\frac{\sqrt{x}+1}{\left(\sqrt{x}\right)^2+2\sqrt{x}+1}\right)\)\(\times\frac{x-1}{\sqrt{x}-3}\)

\(\Leftrightarrow\left(\frac{1}{\sqrt{x}-1}-\frac{\sqrt{x}+1}{\left(\sqrt{x}+1\right)^2}\right)\)\(\times\frac{x-1}{\sqrt{x}-3}\)(1)

Để A xđ <=> \(\hept{\begin{cases}x\ge0\\\sqrt{x}-1\ne0\\\sqrt{x}-3\ne0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ge0\\x\ne1\\x\ne9\end{cases}}\)

b , (1) <=> \(\left(\frac{\left(\sqrt{x}+1\right)^2-\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2}\right)\)\(\times\frac{x-1}{\sqrt{x}-3}\)

<=> \(\left(\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+1-\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2}\right)\)\(\times\frac{x-1}{\sqrt{x}-3}\)

<=> \(\frac{2}{x-1}\times\frac{x-1}{\sqrt{x}-3}\)

<=> \(\frac{2}{\sqrt{x}-3}\)