Question

Дам 50 баллов. Упростить выражение. Хочу себя проверить​

Answer 1

$dfrac{sqrt{2}}{sqrt{8}+2}-dfrac{6-sqrt{32}}{sqrt{8}-3}=dfrac{sqrt{2}}{2sqrt{2}+2}-dfrac{6-4sqrt{2}}{2sqrt{2}-3}=dfrac{1}{2+sqrt{2}}+dfrac{2(3-2sqrt{2})}{3-2sqrt{2}}= \ =dfrac{1}{2+sqrt{2}}+2=dfrac{5+2sqrt{2}}{2+sqrt{2}}=dfrac{(5+2sqrt{2})(2-sqrt{2})}{4-2}=dfrac{10+4sqrt{2}-5sqrt{2}-4}{2}= \ =dfrac{6-sqrt{2}}{2}$