[tex] \frac{5}{3 \sqrt{3} - \sqrt{6} } = [/tex]
[tex] \frac{5}{3 \sqrt{3} - \sqrt{6} } · \frac{3 \sqrt{3} + \sqrt{6} }{3 \sqrt{3} + \sqrt{?} } = [/tex]
[tex] \frac{5(3 \sqrt{3} + \sqrt{6} )}{(3 \sqrt{3} - \sqrt{6})(3 \sqrt{3} + \sqrt{6} )} = [/tex]
[tex] \frac{5(3 \sqrt{3} + \sqrt{6}) }{( {3 \sqrt{3} )}^{2} - {( \sqrt{6} )}^{2} } = [/tex]
[tex] \frac{15 \sqrt{3} + 5 \sqrt{6} }{27 - 6} = [/tex]
[tex] \frac{15 \sqrt{5} + 5 \sqrt{6} }{21} [/tex]
[tex] \frac{ \sqrt{7} }{ \sqrt{5} - \sqrt{2} } = [/tex]
[tex] \frac{ \sqrt{7} }{ \sqrt{5} - \sqrt{2} } · \frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} + \sqrt{2} } = [/tex]
[tex] \frac{ \sqrt{7} ( \sqrt{5} + \sqrt{2} )}{ (\sqrt{5} - \sqrt{2})( \sqrt{5} + \sqrt{2} ) } = [/tex]
[tex] \frac{ \sqrt{7}( \sqrt{5} + \sqrt{2} )}{ {( \sqrt{5}) }^{2} - { (\sqrt{2} )}^{2} } = [/tex]
[tex] \frac{ \sqrt{35} + \sqrt{14} }{5 - 2} = [/tex]
[tex] \frac{ \sqrt{35} + \sqrt{14} }{3} [/tex]
[tex] \frac{2 \sqrt{6} }{5 \sqrt{3} - \sqrt{5} } = [/tex]
[tex] \frac{2 \sqrt{6} }{5 \sqrt{3} - \sqrt{5} } · \frac{5 \sqrt{3} + \sqrt{5} }{5 \sqrt{3} + \sqrt{5} } = [/tex]
[tex] \frac{2 \sqrt{6}(5 \sqrt{3} + \sqrt{5} ) }{(5 \sqrt{3} - \sqrt{5})(5 \sqrt{3} + \sqrt{5} )} = [/tex]
[tex] \frac{2 \sqrt{6}(5 \sqrt{3} + \sqrt{5} ) }{ {( 5\sqrt{3} )}^{2} - { (\sqrt{5}) }^{2} } = [/tex]
[tex] \frac{10 \sqrt{18} + 2 \sqrt{30} }{75 - 5} = [/tex]
[tex] \frac{10 \sqrt{18} + 2 \sqrt{30} }{70} = [/tex]
[tex] \frac{5 \sqrt{18} + \sqrt{30} }{35} = [/tex]
[tex] \frac{5 \sqrt{9·2} + \sqrt{30} }{35} = [/tex]
[tex] \frac{5 \sqrt{9} \sqrt{2} + \sqrt{30} }{35} = [/tex]
[tex] \frac{5·3 \sqrt{2} + \sqrt{30} }{35} = [/tex]
[tex] \frac{15 \sqrt{2} + \sqrt{30} }{35} [/tex]
[tex] \frac{ \sqrt{3} }{ \sqrt{8} - \sqrt{6} } = [/tex]
[tex] \frac{ \sqrt{3} }{ \sqrt{8} - \sqrt{6} } · \frac{ \sqrt{8} + \sqrt{6} }{ \sqrt{8} + \sqrt{6} } = [/tex]
[tex] \frac{ \sqrt{3} ( \sqrt{8} + \sqrt{6}) }{( \sqrt{8} - \sqrt{6} )( \sqrt{8} + \sqrt{6} ) } = [/tex]
[tex] \frac{ \sqrt{3}( \sqrt{8} + \sqrt{6}) }{ { (\sqrt{8} )}^{2} - { (\sqrt{6} )}^{2} } = [/tex]
[tex] \frac{ \sqrt{24} + \sqrt{18} }{8 - 6} = [/tex]
[tex] \frac{ \sqrt{24} + \sqrt{18} }{2} = [/tex]
[tex] \frac{ \sqrt{4·6} + \sqrt{9·2} }{2} = [/tex]
[tex] \frac{ \sqrt{4} \sqrt{6} + \sqrt{9} \sqrt{2} }{2} = [/tex]
[tex] \frac{2 \sqrt{6} + 3 \sqrt{2} }{2} [/tex]
[tex] \frac{4 \sqrt{5} }{ \sqrt{21} - \sqrt{11} } = [/tex]
[tex] \frac{4 \sqrt{5} }{ \sqrt{21} - \sqrt{11} } · \frac{ \sqrt{21} + \sqrt{11} }{ \sqrt{21} + \sqrt{11} } = [/tex]
[tex] \frac{4 \sqrt{5}( \sqrt{21} + \sqrt{11} )}{( \sqrt{21} - \sqrt{11} )( \sqrt{21} + \sqrt{11} ) } = [/tex]
[tex] \frac{4 \sqrt{5} ( \sqrt{21} - \sqrt{11}) }{ { (\sqrt{21}) }^{2} - {( \sqrt{11} )}^{2} } = [/tex]
[tex] \frac{4 \sqrt{105} - 4 \sqrt{55} }{21 - 11} = [/tex]
[tex] \frac{4 \sqrt{105} - 4 \sqrt{55} }{10} = [/tex]
[tex] \frac{2 \sqrt{105} - 2 \sqrt{55} }{5} [/tex]
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1
[tex] \frac{5}{3 \sqrt{3} - \sqrt{6} } = [/tex]
[tex] \frac{5}{3 \sqrt{3} - \sqrt{6} } · \frac{3 \sqrt{3} + \sqrt{6} }{3 \sqrt{3} + \sqrt{?} } = [/tex]
[tex] \frac{5(3 \sqrt{3} + \sqrt{6} )}{(3 \sqrt{3} - \sqrt{6})(3 \sqrt{3} + \sqrt{6} )} = [/tex]
[tex] \frac{5(3 \sqrt{3} + \sqrt{6}) }{( {3 \sqrt{3} )}^{2} - {( \sqrt{6} )}^{2} } = [/tex]
[tex] \frac{15 \sqrt{3} + 5 \sqrt{6} }{27 - 6} = [/tex]
[tex] \frac{15 \sqrt{5} + 5 \sqrt{6} }{21} [/tex]
2
[tex] \frac{ \sqrt{7} }{ \sqrt{5} - \sqrt{2} } = [/tex]
[tex] \frac{ \sqrt{7} }{ \sqrt{5} - \sqrt{2} } · \frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} + \sqrt{2} } = [/tex]
[tex] \frac{ \sqrt{7} ( \sqrt{5} + \sqrt{2} )}{ (\sqrt{5} - \sqrt{2})( \sqrt{5} + \sqrt{2} ) } = [/tex]
[tex] \frac{ \sqrt{7}( \sqrt{5} + \sqrt{2} )}{ {( \sqrt{5}) }^{2} - { (\sqrt{2} )}^{2} } = [/tex]
[tex] \frac{ \sqrt{35} + \sqrt{14} }{5 - 2} = [/tex]
[tex] \frac{ \sqrt{35} + \sqrt{14} }{3} [/tex]
3
[tex] \frac{2 \sqrt{6} }{5 \sqrt{3} - \sqrt{5} } = [/tex]
[tex] \frac{2 \sqrt{6} }{5 \sqrt{3} - \sqrt{5} } · \frac{5 \sqrt{3} + \sqrt{5} }{5 \sqrt{3} + \sqrt{5} } = [/tex]
[tex] \frac{2 \sqrt{6}(5 \sqrt{3} + \sqrt{5} ) }{(5 \sqrt{3} - \sqrt{5})(5 \sqrt{3} + \sqrt{5} )} = [/tex]
[tex] \frac{2 \sqrt{6}(5 \sqrt{3} + \sqrt{5} ) }{ {( 5\sqrt{3} )}^{2} - { (\sqrt{5}) }^{2} } = [/tex]
[tex] \frac{10 \sqrt{18} + 2 \sqrt{30} }{75 - 5} = [/tex]
[tex] \frac{10 \sqrt{18} + 2 \sqrt{30} }{70} = [/tex]
[tex] \frac{5 \sqrt{18} + \sqrt{30} }{35} = [/tex]
[tex] \frac{5 \sqrt{9·2} + \sqrt{30} }{35} = [/tex]
[tex] \frac{5 \sqrt{9} \sqrt{2} + \sqrt{30} }{35} = [/tex]
[tex] \frac{5·3 \sqrt{2} + \sqrt{30} }{35} = [/tex]
[tex] \frac{15 \sqrt{2} + \sqrt{30} }{35} [/tex]
4
[tex] \frac{ \sqrt{3} }{ \sqrt{8} - \sqrt{6} } = [/tex]
[tex] \frac{ \sqrt{3} }{ \sqrt{8} - \sqrt{6} } · \frac{ \sqrt{8} + \sqrt{6} }{ \sqrt{8} + \sqrt{6} } = [/tex]
[tex] \frac{ \sqrt{3} ( \sqrt{8} + \sqrt{6}) }{( \sqrt{8} - \sqrt{6} )( \sqrt{8} + \sqrt{6} ) } = [/tex]
[tex] \frac{ \sqrt{3}( \sqrt{8} + \sqrt{6}) }{ { (\sqrt{8} )}^{2} - { (\sqrt{6} )}^{2} } = [/tex]
[tex] \frac{ \sqrt{24} + \sqrt{18} }{8 - 6} = [/tex]
[tex] \frac{ \sqrt{24} + \sqrt{18} }{2} = [/tex]
[tex] \frac{ \sqrt{4·6} + \sqrt{9·2} }{2} = [/tex]
[tex] \frac{ \sqrt{4} \sqrt{6} + \sqrt{9} \sqrt{2} }{2} = [/tex]
[tex] \frac{2 \sqrt{6} + 3 \sqrt{2} }{2} [/tex]
5
[tex] \frac{4 \sqrt{5} }{ \sqrt{21} - \sqrt{11} } = [/tex]
[tex] \frac{4 \sqrt{5} }{ \sqrt{21} - \sqrt{11} } · \frac{ \sqrt{21} + \sqrt{11} }{ \sqrt{21} + \sqrt{11} } = [/tex]
[tex] \frac{4 \sqrt{5}( \sqrt{21} + \sqrt{11} )}{( \sqrt{21} - \sqrt{11} )( \sqrt{21} + \sqrt{11} ) } = [/tex]
[tex] \frac{4 \sqrt{5} ( \sqrt{21} - \sqrt{11}) }{ { (\sqrt{21}) }^{2} - {( \sqrt{11} )}^{2} } = [/tex]
[tex] \frac{4 \sqrt{105} - 4 \sqrt{55} }{21 - 11} = [/tex]
[tex] \frac{4 \sqrt{105} - 4 \sqrt{55} }{10} = [/tex]
[tex] \frac{2 \sqrt{105} - 2 \sqrt{55} }{5} [/tex]