Question

Tính

Answer 1

\(A=\dfrac{\sqrt{2}-1-\sqrt{2}+\left(\sqrt{2}+1\right)^2}{\sqrt{2}\left(\sqrt{2}+1\right)}\\ A=\dfrac{-1+3+2\sqrt{2}}{\sqrt{2}\left(\sqrt{2}+1\right)}=\dfrac{2+2\sqrt{2}}{\sqrt{2}\left(\sqrt{2}+1\right)}=\dfrac{2\left(\sqrt{2}+1\right)}{\sqrt{2}\left(\sqrt{2}+1\right)}\\ A=\sqrt{2}\)

Answer 2

\(A=\dfrac{\sqrt{2}-1}{2+\sqrt{2}}-\dfrac{1}{\sqrt{2}+1}+\dfrac{\sqrt{2}+1}{\sqrt{2}}\)

\(=\dfrac{\sqrt{2}-1-\sqrt{2}+3+2\sqrt{2}}{2+\sqrt{2}}\)

\(=\dfrac{2\sqrt{2}+2}{2+\sqrt{2}}=\sqrt{2}\)