= [tex]\frac{3b(b^2+\sqrt{3})-3(3b^2-3b+1)}{3b^2-2\sqrt{3}b+1}[/tex]= [tex]\frac{3b(b-\sqrt{3})(b+\sqrt{3})-3(b-1)^2}{3b^2-2\sqrt{3}b+1}[/tex]= [tex]\frac{3b(b-\sqrt{3})(b+\sqrt{3})-3(b-1)^2}{(3b-1)(b-\sqrt{3})}[/tex]= [tex]\frac{3(b-1)(b+\sqrt{3})}{3b-1}[/tex]= [tex]b+\sqrt{3}[/tex]
= [tex]\frac{3b(b^2+\sqrt{3})-3(3b^2-3b+1)}{3b^2-2\sqrt{3}b+1}[/tex]
= [tex]\frac{3b(b-\sqrt{3})(b+\sqrt{3})-3(b-1)^2}{3b^2-2\sqrt{3}b+1}[/tex]
= [tex]\frac{3b(b-\sqrt{3})(b+\sqrt{3})-3(b-1)^2}{(3b-1)(b-\sqrt{3})}[/tex]
= [tex]\frac{3(b-1)(b+\sqrt{3})}{3b-1}[/tex]
= [tex]b+\sqrt{3}[/tex]