Find perfect squares in each radical.

$\sqrt{(4)(3)}+\frac{\sqrt3}{2}-\sqrt{(9)(3)}$

Take the roots placing them outside of the radical.

$2\sqrt{3}+\frac{\sqrt3}{2}-3\sqrt3$

$\text{Combine the }\sqrt{3}\text{'s}$

$-\frac{\sqrt3}{2}$

Multiply the factors. Remember the middle terms.
Simplify by adding like terms.

$5-2\sqrt6$