Obliczenia
[tex]\frac{\sqrt3}{1-\frac{1}{\sqrt3}}=\frac{\sqrt3}{1-\frac{1}{\sqrt3}}\cdot\frac{1+\frac{1}{\sqrt3}}{1+\frac{1}{\sqrt3}}=\frac{\sqrt3(1+\frac{1}{\sqrt3})}{(1-\frac{1}{\sqrt3})(1+\frac{1}{\sqrt3})}=\frac{\sqrt3+\frac{\sqrt3}{\sqrt3}}{1^2-(\frac{1}{\sqrt3})^2}=\\\\\\=\frac{\sqrt3+1}{1-\frac{1}{3}}=\frac{\sqrt3+1}{\frac{2}{3}}=\frac{\sqrt3+1}{1}\cdot\frac{3}{2}=\boxed{\frac{3\sqrt3+3}{2}}[/tex]
