\left( \dfrac{ 1 }{ \sqrt{ x \phantom{\tiny{!}}} -1 } - \dfrac{ 1 }{ \sqrt{ x \phantom{\tiny{!}}} } \right) \left( \dfrac{ \sqrt{ x \phantom{\tiny{!}}} +1 }{ \sqrt{ x \phantom{\tiny{!}}} -2 } - \dfrac{ \sqrt{ x \phantom{\tiny{!}}} +2 }{ \sqrt{ x \phantom{\tiny{!}}} -1 } \right)
Rút Gọn
Tìm x đễ biêu thức âm
\( \left( \dfrac{ 1 }{ \sqrt{ x \phantom{\tiny{!}}} -1 } - \dfrac{ 1 }{ \sqrt{ x \phantom{\tiny{!}}} } \right) \left( \dfrac{ \sqrt{ x \phantom{\tiny{!}}} +1 }{ \sqrt{ x \phantom{\tiny{!}}} -2 } - \dfrac{ \sqrt{ x \phantom{\tiny{!}}} +2 }{ \sqrt{ x \phantom{\tiny{!}}} -1 } \right) \)
\(=\left(\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right)\left(\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}-\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\right)\)
\(=\dfrac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}\left(\dfrac{x-1}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}-\dfrac{x-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\right)\)
\(=\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}.\dfrac{3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{3}{\sqrt{x}\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)^2}\)
