từ dòng cuối là sai rồi bạn à

Bạn bỏ dòng cuối đi còn lại đúng rồi

Ở tử đặt nhân tử chung căn x chung  rồi lại đặt căn x +1 chung

Ở mẫu tách 3 căn x ra 2 căn x +căn x rồi đặt nhân tử 2 căn x ra 

rút gọn được \(\frac{3\sqrt{x}-5}{2\sqrt{x}+1}\)

cảm ơn bạn nha 

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

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

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

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

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

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

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

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

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

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

Thay \(x=\frac{1}{2}\left(1+\sqrt{2}\right)^2\) vào \(M=-\sqrt{2x}\) ta được:

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

\(M=-1-\sqrt{2}\)

Vậy ..............

Rút gọn P

đk: \(\hept{\begin{cases}x\ge0\\x\ne1\end{cases}}\)

Ta có:

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

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

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

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

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