Question

Tìm ĐKXĐ và rút gọn:

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

Answer 1

điều kiện : \(x>0;x\ne1\)

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

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

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