\(\left(\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+1}\right)\left(\frac{x-1}{\sqrt{x}+1}-2\right)\left(ĐK:x\ne\pm1\right)\)

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

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

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

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

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

\(=\frac{2\sqrt{x}-6}{x-1}\)

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

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

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

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

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

\(=\frac{2x\sqrt{x}-6\sqrt{x}-4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2}\)

Bài lm có sai sót chỗ nào thì mong bn sửa lại........

\(\frac{x-3\sqrt{x}}{\sqrt{x}-3}-\frac{x-4\sqrt{x}+3}{\sqrt{x}+3}=\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{\sqrt{x}-3}-\frac{x-3\sqrt{x}-\sqrt{x}+3}{\sqrt{x}+3}\)

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

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

\(=\frac{x+3\sqrt{x}-x+4\sqrt{x}-3}{\sqrt{x}+3}\)

\(=\frac{7\sqrt{x}-3}{\sqrt{x}+3}\)

\(\frac{x-3\sqrt{x}}{\sqrt{x}-3}-\frac{x+4\sqrt{x}+3}{\sqrt{x}+3}\)

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

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

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

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

Khó quá 

\(a,\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)

\(=\sqrt{5-2\sqrt{5}+1}+\sqrt{5+2\sqrt{5}+1}\)

\(=\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}\)

\(=\sqrt{5}-1+\sqrt{5}+1\)

\(=2\sqrt{5}\)

\(b,\sqrt{9-4\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)(Đề sai sửa lại)

\(=\sqrt{5-2.2\sqrt{5}+4}+\sqrt{5+2.2\sqrt{5}+4}\)

\(=\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{\left(\sqrt{5}+2\right)^2}\)

\(=\sqrt{5}-2+\sqrt{5}+2\)

\(=2\sqrt{5}\)

\(x-5\sqrt{x-2}=-2\)

\(\Leftrightarrow-5\sqrt{x-2}=-2-x\)

\(\Leftrightarrow\left(-5\sqrt{x-2}\right)^2=-2x-x\)

<=> 25x - 50 = 4 + 4x + x²

<=> x = 18 hoặc x = 3

Vậy:...

\(DKXĐ:x\ge2\)

\(x-5\sqrt{x-2}=-2\)

\(\Leftrightarrow5\sqrt{x-2}=x+2\)

\(\Leftrightarrow25\left(x-2\right)=\left(x+2\right)^2\)

\(\Leftrightarrow25x-50=x^2+4x+4\)

\(\Leftrightarrow x^2+4x+4-25x+50=0\)

\(\Leftrightarrow x^2-21x+54=0\)

\(\Leftrightarrow\left(x-18\right)\left(x-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-18=0\\x-3=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=18\\x=3\end{cases}\left(\frac{t}{m}ĐKXĐ\right)}\)

mình cần gấp, thanks các bạn

Đề chắc chắn đúng chứ bạn??

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

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

\(\Rightarrow2x-3=4\left(x-1\right)\)

\(\Rightarrow2x-3=4x-4\)

\(\Rightarrow4x-2x=4-3\)

\(\Rightarrow2x=1\)

\(\Rightarrow x=\frac{1}{2}\)

\(ĐKXĐ:\hept{\begin{cases}x-1>0\\2x-3\ge0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x>1\\x>\frac{3}{2}\end{cases}}\)

\(\Leftrightarrow x>\frac{3}{2}\)

Vậy nên \(x=\frac{1}{2}\) không thỏa mãn ĐKXĐ.