A binary operation is defined as p q = (3p + 2q)/(2p + 3q). a) Evaluate (sqrt(3)) (sqrt(2)). b) Find the value of x for which x * 3 = (1)/(2).

\begin{align*} (\sqrt{3}) * (\sqrt{2}) &= \frac{3\sqrt{3} + 2\sqrt{2}}{2\sqrt{3} + 3\sqrt{2}} \times \frac{2\sqrt{3} - 3\sqrt{2}}{2\sqrt{3} - 3\sqrt{2}} \ &= \frac{(3\sqrt{3})(2\sqrt{3}) - (3\sqrt{3})(3\sqrt{2}) + (2\sqrt{2})(2\sqrt{3}) - (2\sqrt{2})(3\sqrt{2})}{(2\sqrt{3})^2 - (3\sqrt{2})^2} \ &= \frac{6(3) - 9\sqrt{6} + 4\sqrt{6} - 6(2)}{4(3) - 9(2)} \ &= \frac{18 - 9\sqrt{6} + 4\sqrt{6} - 12}{12 - 18} \ &= \frac{6 - 5\sqrt{6}}{-6}\end{align*}

The value is $\boxed{\frac{5\sqrt{6} - 6}{6}}$.

The value of $x$ is $\boxed{-\frac{3}{4}}$.