mn làm hộ mik vs ak mik đg cần gấp lắm Cảm ơn mn trước nha Question mn làm hộ mik vs ak mik đg cần gấp lắm Cảm ơn mn trước nha in progress 0 Môn Toán Ladonna 4 years 2020-11-24T16:49:24+00:00 2020-11-24T16:49:24+00:00 1 Answers 52 views 0
Answers ( )
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
9,\\
O = \left( {\dfrac{1}{{\sqrt x – 1}} + \dfrac{1}{{\sqrt x + 1}}} \right).\dfrac{{\sqrt x – 1}}{2}\\
= \dfrac{{\left( {\sqrt x + 1} \right) + \left( {\sqrt x – 1} \right)}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{\sqrt x – 1}}{2}\\
= \dfrac{{2\sqrt x }}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{\sqrt x – 1}}{2}\\
= \dfrac{{\sqrt x }}{{\sqrt x + 1}}\\
10,\\
I = \left( {\dfrac{{\sqrt x }}{{x – 4}} + \dfrac{1}{{\sqrt x – 2}}} \right):\dfrac{2}{{\sqrt x – 2}}\\
= \left( {\dfrac{{\sqrt x }}{{\left( {\sqrt x – 2} \right)\left( {\sqrt x + 2} \right)}} + \dfrac{1}{{\sqrt x – 2}}} \right).\dfrac{{\sqrt x – 2}}{2}\\
= \left( {\dfrac{{\sqrt x + \left( {\sqrt x + 2} \right)}}{{\left( {\sqrt x – 2} \right)\left( {\sqrt x + 2} \right)}}} \right).\dfrac{{\sqrt x – 2}}{2}\\
= \dfrac{{2\sqrt x + 2}}{{\left( {\sqrt x – 2} \right)\left( {\sqrt x + 2} \right)}}.\dfrac{{\sqrt x – 2}}{2}\\
= \dfrac{{\sqrt x + 1}}{{\sqrt x + 2}}\\
11,\\
J = \left( {\dfrac{{\sqrt x }}{{x – 9}} – \dfrac{1}{{\sqrt x + 3}}} \right):\left( {\dfrac{1}{{\sqrt x – 3}} – \dfrac{1}{{\sqrt x }}} \right)\\
= \left( {\dfrac{{\sqrt x }}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x + 3} \right)}} – \dfrac{1}{{\sqrt x + 3}}} \right):\dfrac{{\sqrt x – \left( {\sqrt x – 3} \right)}}{{\left( {\sqrt x – 3} \right).\sqrt x }}\\
= \dfrac{{\sqrt x – \left( {\sqrt x – 3} \right)}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x + 3} \right)}}:\dfrac{3}{{\sqrt x \left( {\sqrt x – 3} \right)}}\\
= \dfrac{3}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x + 3} \right)}}.\dfrac{{\sqrt x \left( {\sqrt x – 3} \right)}}{3}\\
= \dfrac{{\sqrt x }}{{\sqrt x + 3}}\\
12,\\
P = \dfrac{{\sqrt x + 1}}{{x – 1}} – \dfrac{{x + 2}}{{x\sqrt x – 1}} – \dfrac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\\
= \dfrac{{\sqrt x + 1}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}} – \dfrac{{x + 2}}{{\left( {\sqrt x – 1} \right)\left( {x + \sqrt x + 1} \right)}} – \dfrac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\\
= \dfrac{1}{{\sqrt x – 1}} – \dfrac{{x + 2}}{{\left( {\sqrt x – 1} \right)\left( {x + \sqrt x + 1} \right)}} – \dfrac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\\
= \dfrac{{\left( {x + \sqrt x + 1} \right) – \left( {x + 2} \right) – \left( {\sqrt x + 1} \right)\left( {\sqrt x – 1} \right)}}{{\left( {\sqrt x – 1} \right)\left( {x + \sqrt x + 1} \right)}}\\
= \dfrac{{x + \sqrt x + 1 – x – 2 – x + 1}}{{\left( {\sqrt x – 1} \right)\left( {x + \sqrt x + 1} \right)}}\\
= \dfrac{{ – x + \sqrt x }}{{\left( {\sqrt x – 1} \right)\left( {x + \sqrt x + 1} \right)}}\\
= \dfrac{{ – \sqrt x }}{{x + \sqrt x + 1}}
\end{array}\)