Помогите решить. [latex] frac{(5 sqrt{3}+ sqrt{50})(5- sqrt{24})}{ sqrt{75}-5 sqrt{2} } [/latex]

[latex] frac{(5 sqrt{3}+ sqrt{50} )(5- sqrt{24}) }{ sqrt{75} -5 sqrt{2} }=frac{5sqrt{3} -5 sqrt{2} }{5sqrt{3} -5 sqrt{2} } =1[/latex][latex]\ \ (5 sqrt{3} + sqrt{50} )(5- sqrt{24} )= \ =25 sqrt{3} -5 sqrt{72} +5 sqrt{50} - sqrt{1200} = \ =25 sqrt{3} -5 sqrt{36*2} +5 sqrt{25*5} - \ - sqrt{400*3} =25 sqrt{3} -5*6 sqrt{2} + \ +5*5 sqrt{2} -20 sqrt{3} =25 sqrt{3} -30 sqrt{2} + \ +25 sqrt{2} -20 sqrt{3} =25 sqrt{3} -20 sqrt{3} + \ +25 sqrt{2} -30 sqrt{2} =5 sqrt{3} -5 sqrt{2} \ \ sqrt{75} -5 sqrt{2} = sqrt{25*3} -5 sqrt{2} = \ =5 sqrt{3} -5 sqrt{2} \ \ [/latex]

[latex] frac{(5 sqrt{3}+ sqrt{50 })(5- sqrt{24}) }{ sqrt{75} -5 sqrt{2} } = \ = frac{(5 sqrt{3}+5 sqrt{2})(5-2 sqrt{6}) }{5 sqrt{3}-5 sqrt{2} } } = frac{(5 sqrt{3}+5 sqrt{2})^2(5-2 sqrt{6} ) }{25*3-25*2} = \ = frac{(75+50 sqrt{6}+50)(5-2 sqrt{6} ) }{75-50} = frac{(125+50 sqrt{6})(5-2 sqrt{6} ) }{25}= \ = frac{625-250 sqrt{6}+250 sqrt{6}-600 }{25}= frac{25}{25}=1 [/latex]