Toán Lớp 9: (3-√3)/(1-√3)+ 2/(2√2+3)+ 4/(√2)
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Toán Lớp 9: (3-√3)/(1-√3)+ 2/(2√2+3)+ 4/(√2)
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\dfrac{{3 – \sqrt 3 }}{{1 – \sqrt 3 }} + \dfrac{2}{{2\sqrt 3 + 3}} + \dfrac{4}{{\sqrt 2 }}\\
= \dfrac{{{{\sqrt 3 }^2} – \sqrt 3 }}{{1 – \sqrt 3 }} + \dfrac{{2.\left( {3 – 2\sqrt 2 } \right)}}{{\left( {3 + 2\sqrt 2 } \right)\left( {3 – 2\sqrt 2 } \right)}} + \dfrac{{2.2}}{{\sqrt 2 }}\\
= \dfrac{{\sqrt 3 \left( {\sqrt 3 – 1} \right)}}{{1 – \sqrt 3 }} + \dfrac{{2.\left( {3 – 2\sqrt 2 } \right)}}{{{3^2} – {{\left( {2\sqrt 2 } \right)}^2}}} + \dfrac{{2.{{\sqrt 2 }^2}}}{{\sqrt 2 }}\\
= – \sqrt 3 + \dfrac{{6 – 4\sqrt 2 }}{{9 – 8}} + 2\sqrt 2 \\
= – \sqrt 3 + \dfrac{{6 – 4\sqrt 2 }}{1} + 2\sqrt 2 \\
= – \sqrt 3 + 6 – 4\sqrt 2 + 2\sqrt 2 \\
= 6 – 2\sqrt 2 – \sqrt 3
\end{array}\)