Question

1)3√30-2√42

   ----------------

   √45-√28

2)

7-3√2

---------  + 7+3√2 / 7-3√2

7+3√2

/-знак деления дробью

Answer 1

$frac{3sqrt{30}-2sqrt{42}}{sqrt{45}-sqrt{28}}=frac{3sqrt{6}sqrt{5}-2sqrt{6}sqrt{7}}{3sqrt{5}-2sqrt{7}}=frac{sqrt{6}(sqrt{5}-2sqrt{7})}{3sqrt{5}-2sqrt{7}}=sqrt{6}$

 

$frac{7-3sqrt{2}}{7+3sqrt{2}}+frac{7+3sqrt{2}}{7-3sqrt{2}}=\\=frac{(7-3sqrt{2})^2+(7+3sqrt{2})^2}{(7+3sqrt{2})(7-3sqrt{2})}=frac{(49-42sqrt{2}+18)+(49+42sqrt{2}+18)}{49-18}=\\=frac{134}{31}=4frac{10}{31}$

Answer 2

$frac{3sqrt{30}-2sqrt{42}}{sqrt{45}-sqrt{28}}=\\ frac{3sqrt{5*6}-2sqrt{7*6}}{sqrt{9*5}-sqrt{4*7}}=\\ frac{3sqrt{5}*sqrt{6}-2sqrt{7}*sqrt{6}}{sqrt{9}*sqrt{5}-sqrt{4}*sqrt{7}}=\\ frac{sqrt{6}(3sqrt{5}-2sqrt{7})}{3sqrt{5}-2sqrt{7}}=\\ sqrt{6}$

 

$frac{7-3sqrt{2}}{7+3sqrt{2}}+frac{7+3sqrt{2}}{7-3sqrt{2}}=\\ frac{(7-3sqrt{2})^2}{(7+3sqrt{2})(7-3sqrt{2})}+frac{(7+3sqrt{2})^2}{(7-3sqrt{2})(7+3sqrt{2})}=\\ frac{(7-3sqrt{2})^2+(7+3sqrt{2})^2}{(7-3sqrt{2})(7+3sqrt{2})}=\\ frac{49-42sqrt{2}+18+49+42sqrt{2}+18}{49-18}=\\ frac{134}{31}$