Question

Rút gọn:

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

Answer 1

Điều kiện: \(x>0,x\ne1\)

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

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

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

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

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