Toán Lớp 9: a, $3/(√7-2)+√((√7-3) )^{2}$
b, (√x/(√x-1)-√x/(x-√x)):(√x+1)/(x-1)
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Toán Lớp 9: a, $3/(√7-2)+√((√7-3) )^{2}$
b, (√x/(√x-1)-√x/(x-√x)):(√x+1)/(x-1)
Comments ( 1 )
a)\dfrac{3}{{\sqrt 7 – 2}} + \sqrt {{{\left( {\sqrt 7 – 3} \right)}^2}} \\
= \dfrac{{3\left( {\sqrt 7 + 2} \right)}}{{7 – {2^2}}} + \left| {\sqrt 7 – 3} \right|\\
= \dfrac{{3\left( {\sqrt 7 + 2} \right)}}{{7 – 4}} + 3 – \sqrt 7 \\
= \sqrt 7 + 2 + 3 – \sqrt 7 \\
= 5\\
b)\left( {\dfrac{{\sqrt x }}{{\sqrt x – 1}} – \dfrac{x}{{x – \sqrt x }}} \right):\dfrac{{\sqrt x + 1}}{{x – 1}}\\
= \left( {\dfrac{{\sqrt x }}{{\sqrt x – 1}} – \dfrac{x}{{\sqrt x \left( {\sqrt x – 1} \right)}}} \right):\dfrac{1}{{\sqrt x – 1}}\\
= \left( {\dfrac{{\sqrt x }}{{\sqrt x – 1}} – \dfrac{{\sqrt x }}{{\sqrt x – 1}}} \right).\left( {\sqrt x – 1} \right)\\
= 0.\left( {\sqrt x – 1} \right)\\
= 0
\end{array}$