Bonjour Bonbonharibo
[tex]\dfrac{1+\dfrac{\sqrt{2}}{2}}{\sqrt{2}}=\dfrac{(1+\dfrac{\sqrt{2}}{2})\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\dfrac{1\times\sqrt{2}+\dfrac{\sqrt{2}}{2}\times\sqrt{2}}{(\sqrt{2})^2}\\\\\\=\dfrac{\sqrt{2}+\dfrac{(\sqrt{2})^2}{2}}{2}=\dfrac{\sqrt{2}+\dfrac{2}{2}}{2}=\dfrac{\sqrt{2}+1}{2}=\dfrac{\sqrt{2}}{2}+\dfrac{1}{2}=\boxed{\dfrac{1}{2}\times\sqrt{2}+\dfrac{1}{2}}[/tex]