[latex] frac{3 sqrt{3} }{1- frac{ sqrt{3} }{3} } [/latex] Jak takie coś obliczyć :/

[latex]dfrac{3sqrt{3}}{1-dfrac{sqrt{3}}{3}}=dfrac{3sqrt{3}}{dfrac{3}{3}-dfrac{sqrt{3}}{3}}=dfrac{3sqrt{3}}{dfrac{3-sqrt{3}}{3}}=3sqrt{3}cdot dfrac{3}{3-sqrt{3}}=dfrac{9sqrt{3}}{3-sqrt{3}}=\ =dfrac{9sqrt{3}}{3-sqrt{3}}cdot dfrac{3+sqrt{3}}{3+sqrt{3}}=dfrac{27sqrt{3}+27}{9-3}=dfrac{27sqrt{3}+27}{6}=dfrac{9+9sqrt{3}}{2}[/latex]

[latex]\3 sqrt{3} : dfrac{3- sqrt{3} }{3} =3 sqrt{3} cdot dfrac{3(3+ sqrt{3} )}{(3- sqrt{3} )(3+ sqrt{3} )} = \ \ \ dfrac{3 sqrt{3}cdot3(3+ sqrt{3} ) }{9-3} = dfrac{3 sqrt{3}(3+ sqrt{3} ) }{2} = dfrac{9 sqrt{3}+9 }{2} [/latex]