Toán Lớp 9: rút gọn D= ( căn x-1/ căn x-2 + 5 căn x – 8/ 2 căn x-x) . x + căn x -1/ căn x-4
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Toán Lớp 9: rút gọn D= ( căn x-1/ căn x-2 + 5 căn x – 8/ 2 căn x-x) . x + căn x -1/ căn x-4
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D = \left( {\dfrac{{\sqrt x – 1}}{{\sqrt x – 2}} + \dfrac{{5\sqrt x – 8}}{{2\sqrt x – x}}} \right).\dfrac{{x + \sqrt x – 1}}{{\sqrt x – 4}}\\
= \dfrac{{\sqrt x \left( {\sqrt x – 1} \right) – 5\sqrt x + 8}}{{\sqrt x \left( {\sqrt x – 2} \right)}}.\dfrac{{x + \sqrt x – 1}}{{\sqrt x – 4}}\\
= \dfrac{{x – \sqrt x – 5\sqrt x + 8}}{{\sqrt x \left( {\sqrt x – 2} \right)}}.\dfrac{{x + \sqrt x – 1}}{{\sqrt x – 4}}\\
= \dfrac{{x – 6\sqrt x + 8}}{{\sqrt x \left( {\sqrt x – 2} \right)}}.\dfrac{{x + \sqrt x – 1}}{{\sqrt x – 4}}\\
= \dfrac{{\left( {\sqrt x – 2} \right)\left( {\sqrt x – 4} \right)}}{{\sqrt x \left( {\sqrt x – 2} \right)}}.\dfrac{{x + \sqrt x – 1}}{{\sqrt x – 4}}\\
= \dfrac{{x + \sqrt x – 1}}{{\sqrt x }}
\end{array}$