Question

Дам 50 баллов. Упростить выражение. Хочу себя проверить​

Answer 1

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