1. (10 points) The value of the expression $\frac{46}{75} \div\left(\frac{5}{12}+\frac{11}{15}\right)-\frac{12}{55}$ is
【Analysis】First calculate the addition inside the parentheses, then perform the division, and finally the subtraction.
【Solution】Solution:
$$
\begin{array}{l}
\frac{46}{75} \div\left(\frac{5}{12}+\frac{11}{15}\right)-\frac{12}{55} \\
=\frac{46}{75} \div \frac{23}{20}-\frac{12}{55} \\
=\frac{8}{15}-\frac{12}{55} \\
=\frac{52}{165}
\end{array}
$$

Therefore, the answer is: $\frac{52}{165}$.