Question

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

Answer 1

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

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

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

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