Question

Rút gọn biểu thức sau

P= (\(\dfrac{1}{x-\sqrt{x}}\) + \(\dfrac{1}{\sqrt{x}-1}\)) : \(\dfrac{\sqrt{x}}{x-2\sqrt{x}+1}\)

Answer 1

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

\(P=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)^2}\)

\(P=\dfrac{1+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}.\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}}\)

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

\(P=\dfrac{\left(\sqrt{x}\right)^2-1^2}{x}=\dfrac{x-1}{x}\)

Answer 2

\(\dfrac{x-1}{x}\)