Toán Lớp 9: P=(1/√x-1+x+√x+2/x-1):1/√x-1
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Toán Lớp 9: P=(1/√x-1+x+√x+2/x-1):1/√x-1
Rút gọn p
Comments ( 1 )
Dkxd:x \ge 0;x \ne 1\\
P = \left( {\dfrac{1}{{\sqrt x – 1}} – \dfrac{{x + \sqrt x + 2}}{{x – 1}}} \right):\dfrac{1}{{\sqrt x – 1}}\\
= \left( {\dfrac{1}{{\sqrt x – 1}} – \dfrac{{x + \sqrt x + 2}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}} \right).\left( {\sqrt x – 1} \right)\\
= \dfrac{{\sqrt x + 1 – x – \sqrt x – 2}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}.\left( {\sqrt x – 1} \right)\\
= \dfrac{{ – x – 1}}{{\sqrt x + 1}}\\
= – \dfrac{{x + 1}}{{\sqrt x + 1}}
\end{array}$