Question

Cho biểu thức A=

\((\dfrac{1}{x-\sqrt{X}}-\dfrac{1}{1-\sqrt{X}})\: :\: \dfrac{\sqrt{X}+1}{x-2\sqrt{X}+1}\) a) Rút gọn

b) Tìm x để A>0

Answer 1

ĐKXĐ : \(\left\{{}\begin{matrix}x\ge0\\x\ne0\\x\ne1\end{matrix}\right.\)

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

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

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

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