Question

Rút gọn biểu thức B=\(\left(\dfrac{\sqrt{x}}{\sqrt{x-1}}+\dfrac{\sqrt{x}}{x-\sqrt{x}}\right)\div\dfrac{\sqrt{x+1}}{x-1}\)

Answer 1

ĐKXĐ: \(x>1\)

Sửa đề: \(B=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{x-\sqrt{x}}\right):\dfrac{\sqrt{x}+1}{x-1}\)

\(=\left[\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\right]:\dfrac{\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)

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

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

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