Question

$frac{1- sqrt{21} }{ sqrt{3}+ sqrt{7} } + frac{26}{3 sqrt{3}-1 }- sqrt{21}-( sqrt{7} -1)(1- sqrt{3} )=$

помогите вычеслить пожалуйста

Answer 1

$frac{1-sqrt{21}}{sqrt{3}+sqrt{7}}+frac{26}{3sqrt{3}-1}-sqrt{21}-(sqrt{7}-1)(1-sqrt{3})= \ \ =frac{1-sqrt{21}}{sqrt{3}+sqrt{7}}+frac{26}{3sqrt{3}-1}-sqrt{21}-(sqrt{7}-sqrt{21}-1+sqrt{3})= \ \ =frac{1-sqrt{21}}{sqrt{3}+sqrt{7}}+frac{26}{3sqrt{3}-1}-sqrt{21}-sqrt{7}+sqrt{21}+1-sqrt{3}= \ \ =frac{1-sqrt{21}}{sqrt{3}+sqrt{7}}+frac{26}{3sqrt{3}-1}-sqrt{7}+1-sqrt{3}= \ \ =frac{1-sqrt{21}}{sqrt{3}+sqrt{7}}+frac{26}{3sqrt{3}-1}-(sqrt{7}-1+sqrt{3})=$

$=frac{(1-sqrt{21})(3sqrt{3}-1)+26(sqrt{3}+sqrt{7})-(-1+sqrt{3}+sqrt{7})(sqrt{3}+sqrt{7})(3sqrt{3}-1)}{(sqrt{3}+sqrt{7})(3sqrt{3}-1)}=$

$=frac{(-1+3sqrt{3}-9sqrt{7}+sqrt{21})+(26sqrt{3}+26sqrt{7})-(-1+sqrt{3}+sqrt{7})(9-sqrt{3}-sqrt{7}+3sqrt{21})}{9-sqrt{3}-sqrt{7}+3sqrt{21}}= \ \ =frac{(-1+3sqrt{3}-9sqrt{7}+sqrt{21})+(26sqrt{3}+26sqrt{7})-(-19+31sqrt{3}+19sqrt{7}-5sqrt{21})}{9-sqrt{3}-sqrt{7}+3sqrt{21}}= \ \ =frac{-1+3sqrt{3}-9sqrt{7}+sqrt{21}+26sqrt{3}+26sqrt{7}+19-31sqrt{3}-19sqrt{7}+5sqrt{21}}{9-sqrt{3}-sqrt{7}+3sqrt{21}}=$

$=frac{18-2sqrt{3}-2sqrt{7}+6sqrt{21}}{9-sqrt{3}-sqrt{7}+3sqrt{21}} =frac{2(9-sqrt{3}-sqrt{7}+3sqrt{21})}{9-sqrt{3}-sqrt{7}+3sqrt{21}}=2$