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Aratati ca [tex] \frac{2}{ \sqrt{3}-1 } - \sqrt{3} = 1[/tex] {help}

Răspuns :

[tex]\dfrac{2}{\sqrt3-1}-\sqrt3=\dfrac{2\cdot(\sqrt3+1)}{(\sqrt3+1)\cdot(\sqrt3-1)}-\sqrt3=\\\\=\dfrac{2\cdot(\sqrt3+1)}{(\sqrt3)^2-1^2}-\sqrt3=\dfrac{2\cdot(\sqrt3+1)}{2}-\sqrt3=\sqrt3+1-\sqrt3=1.[/tex]

Green eyes.