The value of $$\frac{2\frac{1}{3} - 1\frac{2}{11}}{3 + \frac{1}{3 + \frac{1}{3+ \frac{1}{3}}}}$$ is

 $$\frac{2\frac{1}{3} - 1\frac{2}{11}}{3 + \frac{1}{3 + \frac{1}{3+ \frac{1}{3}}}}$$

=  $$\frac{\frac{7}{3} - \frac{13}{11}}{3 + \frac{1}{3 + \frac{1}{\frac{10}{3}}}}$$

=  $$\frac{\frac{77-39}{33}}{3 + \frac{1}{3 + \frac{3}{10}}}$$

=  $$\frac{\frac{38}{33}}{3 + \frac{1}{\frac{33}{10}}}$$

=   $$\frac{\frac{38}{33}}{3 + {\frac{10}{33}}}$$

=  $$\frac{\frac{38}{33}}{\frac{109}{33}}$$

=  $$\frac{38}{109}$$

so the answer is option A.