Question

[Thịnh Gia Vân]

Rút gọn: 

\(\left(\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{x-\sqrt{x}-1}{x-2\sqrt{x}}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}+1}-\frac{x-5}{x-\sqrt{x}-2}\right)\)

Answer 1

[l҉o҉n҉g҉ d҉z҉]

ĐKXĐ : \(\hept{\begin{cases}x>0\\x\ne4\end{cases}}\)

\(=\left(\frac{x}{\sqrt{x}\left(\sqrt{x}-2\right)}-\frac{x-\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\div\left(\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}-\frac{x-5}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\right)\)

\(=\frac{x-x+\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-2\right)}\div\frac{x-4-x+5}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\)

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

Answer 2

[Lê Đức Lương]

\(\left(\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{x-\sqrt{x}-1}{x-2\sqrt{x}}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}+1}-\frac{x-5}{x-\sqrt{x}-2}\right)\)

\(=\left(\frac{x}{\sqrt{x}\left(\sqrt{x}-2\right)}-\frac{x-\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-2\right)}\right):\left(\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}-\frac{x-5}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\right)\)

\(=\frac{\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-2\right)}:\left(\frac{x-4-x+5}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\right)\)

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

\(=\frac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}}\)(p/s: sai thì mong bạn thông cảm nha)