Question

\(\dfrac{1 - \sqrt{x}}{\sqrt{x}(\sqrt{x} + 2 )}\) . \(\dfrac{(\sqrt{x} + 2)^{2}}{1 - \sqrt{x}}\)

Answer 1

\(\dfrac{1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}\cdot\dfrac{\left(\sqrt{x}+2\right)^2}{1-\sqrt{x}}\) (ĐK: \(x>0,x\ne1\))

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

\(=\dfrac{\sqrt{x}+2}{\sqrt{x}}\)

Answer 2

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

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

\(=\dfrac{\sqrt{x}+2}{\sqrt{x}}\)