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