Вычислить [latex]12*( \sqrt[3]{3 \sqrt{3} } - \sqrt[5]{49 \sqrt{7} } ):( \sqrt{3} + \sqrt{7} )-6 \sqrt{21} [/latex]

[latex]12*( \sqrt[3]{3 \sqrt{3} }- \sqrt[5]{49 \sqrt{7} } ):( \sqrt{3}+ \sqrt{7} )-6 \sqrt{21} =[/latex] [latex]=12*\frac{\sqrt[3]{3^1*3^{\frac{1}{2} }}- \sqrt[5]{7^2*7^{\frac{1}{2} } }}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}=12*\frac{\sqrt[3]{3^{1+ \frac{1}{2} }}- \sqrt[5]{7^{2+ \frac{1}{2} } }}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}= [/latex] [latex]=12*\frac{\sqrt[3]{3^{\frac{3}{2} }}- \sqrt[5]{7^{\frac{5}{2} } }}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21} =12*\frac{(3^{\frac{3}{2}})^ \frac{1}{3} - (7^{\frac{5}{2}})^ \frac{1}{5} }{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}= [/latex] [latex]=12*\frac{3^{\frac{3}{2}* \frac{1}{3}} - 7^{\frac{5}{2}*\frac{1}{5}}}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21} =12*\frac{3^{\frac{1}{2}} - 7^{\frac{1}{2}}}{ \sqrt{3}+ \sqrt{7} }-6 \sqrt{21}= [/latex] [latex]=6*2*\frac{ \sqrt{3}- \sqrt{7} }{ \sqrt{3}+ \sqrt{7} }-6* \sqrt{21} =6*(2*\frac{ \sqrt{3}- \sqrt{7} }{ \sqrt{3}+ \sqrt{7} }-\sqrt{21})= [/latex] [latex]=6*(2*\frac{ (\sqrt{3}- \sqrt{7})*(\sqrt{3}- \sqrt{7}) }{ (\sqrt{3}+ \sqrt{7})*(\sqrt{3}- \sqrt{7}) }-\sqrt{21})= [/latex] [latex]=6*(2*\frac{ (\sqrt{3}- \sqrt{7})^2}{3^2-7^2}-\sqrt{21}) =6*(2*\frac{ (\sqrt{3}- \sqrt{7})^2}{9-49}-\sqrt{21})= [/latex] [latex]=6*(2*\frac{ (\sqrt{3})^2-2* \sqrt{3}* \sqrt{7}+( \sqrt{7} )^2}{-40}-\sqrt{21})= [/latex] [latex]=6*(-\frac{2*(3-2* \sqrt{3*7}+7)}{2*20}-\sqrt{21}) =6*(-\frac{7+3-2* \sqrt{21}}{20}-\sqrt{21})= [/latex] [latex]=6*(-\frac{2*5-2* \sqrt{21}}{2*10}-\sqrt{21}) =6*(-\frac{2*(5-\sqrt{21})}{2*10}-\sqrt{21})=[/latex] [latex]=6*(-\frac{5-\sqrt{21}}{10}-\sqrt{21})=-6(\frac{5-\sqrt{21}}{10}+\frac{10*\sqrt{21}}{10})=[/latex] [latex]=-6*\frac{5-\sqrt{21}+10 \sqrt{21} }{10} =-6*\frac{5+9\sqrt{21}}{10} =-\frac{2*3*(5+9\sqrt{21})}{2*5}=[/latex] [latex]=-\frac{3*(5+9\sqrt{21})}{5} =-\frac{3*5+3*9\sqrt{21}}{5} =-\frac{15+27\sqrt{21}}{5}[/latex]