AMC 12 2008a Problem 2

What is the reciprocal of $\frac{1}{2}+\frac{2}{3}$?

$\mathrm{(A)}\ \frac{6}{7} \mathrm{(B)}\ \frac{7}{6} \mathrm{(C)}\ \frac{5}{3} \mathrm{(D)}\ 3 \mathrm{(E)}\ \frac{7}{2}$