express (1-sqrt(3)/(2sqrt(3))+sqrt(3)/2 in a form of a+b sqrt(3)/c

$$Starting with:$$ \frac{1-\sqrt{3}}{2\sqrt{3}}+\frac{\sqrt{3}}{2} $$Multiply left term by $\sqrt{3}$ top and bottom:$$ \frac{(1-\sqrt{3})\sqrt{3}}{6}+\frac{\sqrt{3}}{2} $$Multiply out the bracketed term:$$ \frac{\sqrt{3}-3}{6}+\frac{\sqrt{3}}{2} $$Multiply right term by 3 top and bottom:$$ \frac{\sqrt{3}-3}{6}+\frac{3\sqrt{3}}{6} $$Collect terms:$$ \frac{4\sqrt{3}-3}{6} $$Rewrite as:$$ -\frac{1}{2}+\frac{2\sqrt{3}}{3}

so a is -(1/2), b is 2 and c is 3