Question

[mạc trần]

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

Answer 1

[Minh Nguyen]

Sửa đề :

\(ĐKXĐ:\hept{\begin{cases}x\ge0\\x\ne1\\x\ne9\end{cases}}\)

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

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

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

\(\Leftrightarrow A=\frac{\sqrt{x}}{x+\sqrt{x}+1}\cdot\frac{x+\sqrt{x}+1}{\sqrt{x}-3}\)

\(\Leftrightarrow A=\frac{\sqrt{x}}{\sqrt{x}-3}\)