Toán Lớp 9: P=(√x/√x-1-√x/1+√x):2x√x/1-x
a,rút gọn P
b,tính P khi x=√3
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Toán Lớp 9: P=(√x/√x-1-√x/1+√x):2x√x/1-x
a,rút gọn P
b,tính P khi x=√3
Comments ( 1 )
a)P = \left( {\dfrac{{\sqrt x }}{{\sqrt x – 1}} – \dfrac{{\sqrt x }}{{1 + \sqrt x }}} \right):\dfrac{{2x\sqrt x }}{{1 – x}}\\
= \dfrac{{\sqrt x \left( {1 + \sqrt x } \right) – \sqrt x \left( {\sqrt x – 1} \right)}}{{\left( {\sqrt x – 1} \right)\left( {1 + \sqrt x } \right)}}.\dfrac{{\left( {1 – \sqrt x } \right)\left( {1 + \sqrt x } \right)}}{{2x\sqrt x }}\\
= \dfrac{{\sqrt x + x – x + \sqrt x }}{{ – 1}}.\dfrac{1}{{2x\sqrt x }}\\
= \dfrac{{ – 2\sqrt x }}{{2x\sqrt x }}\\
= – \dfrac{1}{x}\\
b)x = \sqrt 3 \left( {tmdk} \right)\\
P = – \dfrac{1}{{\sqrt 3 }} = – \dfrac{{\sqrt 3 }}{3}
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