[latex] ac{sinalpha+cosalpha}{sinalpha-cosalpha}=(sinalpha+cosalpha):(sinalpha-cosalpha)=\ \ \ =(frac{sqrt{6}}{3}+frac{sqrt{3}}{3}):(frac{sqrt{6}}{3}-frac{sqrt{3}}{3})= frac{sqrt{6}+sqrt{3}}{3}:frac{sqrt{6}-sqrt{3}}{3}=\ \ \ =frac{sqrt{6}+sqrt{3}}{3}*frac{3}{sqrt{6}-sqrt{3}}= frac{sqrt{6}sqrt{3}}{sqrt{6}-sqrt{3}}*frac{sqrt{6}+sqrt{3}}{sqrt{6}+sqrt{3}}=\ \ \ =frac{(sqrt{6}+sqrt{3})^{2}}{sqrt{6}^{2}-sqrt{3}^{2}}= frac{6+2sqrt{6*3}+3}{6-3}=\ [/latex] [latex]=frac{9+2sqrt{9*2}}{3}= frac{9+2*3sqrt{2}}{3}= frac{9+6sqrt{2}}{3}=\ \ =frac{3*(3+2sqrt{2})}{3}= 3+2sqrt{2}[/latex]
