Toán Lớp 9: R = ( √ x – 1 / √ x ) : ( √ x -1 / √ x + 1 – √ x / x- √ x ) giúp em với
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Toán Lớp 9: R = ( √ x – 1 / √ x ) : ( √ x -1 / √ x + 1 – √ x / x- √ x ) giúp em với
Comments ( 1 )
DK:x > 0;x \ne 1\\
R = \left( {\sqrt x – \dfrac{1}{{\sqrt x }}} \right):\left( {\dfrac{{\sqrt x – 1}}{{\sqrt x + 1}} – \dfrac{{\sqrt x }}{{x – \sqrt x }}} \right)\\
= \dfrac{{x – 1}}{{\sqrt x }}:\left( {\dfrac{{\sqrt x – 1}}{{\sqrt x + 1}} – \dfrac{1}{{\sqrt x – 1}}} \right)\\
= \dfrac{{x – 1}}{{\sqrt x }}:\dfrac{{{{\left( {\sqrt x – 1} \right)}^2} – \sqrt x – 1}}{{x – 1}}\\
= \dfrac{{x – 1}}{{\sqrt x }}.\dfrac{{x – 1}}{{x – 2\sqrt x + 1 – \sqrt x – 1}}\\
= \dfrac{{x – 1}}{{\sqrt x }}.\dfrac{{x – 1}}{{x – 3\sqrt x }}\\
= \dfrac{{{{\left( {x – 1} \right)}^2}}}{{x\sqrt x – 3x}}
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