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