Bài giải:

_{$\frac{\left( \frac{1}{6}+\frac{1}{10}+\frac{1}{15} \right):\left( \frac{1}{6}+\frac{1}{10}-\frac{1}{15} \right)}{\left( \frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5} \right):\left( \frac{1}{4}-\frac{1}{6} \right)}=\frac{\left( \frac{5}{30}+\frac{3}{30}+\frac{2}{30} \right):\left( \frac{5}{30}+\frac{3}{30}-\frac{2}{30} \right)}{\left( \frac{30}{60}-\frac{20}{60}+\frac{15}{60}-\frac{12}{60} \right):\left(\frac{3}{12}-\frac{2}{12} \right)}=\frac{\frac{10}{30}:\frac{6}{30}}{\frac{13}{60}:\frac{1}{12}}=\frac{\frac{10}{30}\times \frac{30}{6}}{\frac{13}{60}\times \frac{12}{1}}=\frac{5}{3}:\frac{13}{5}=\frac{25}{39}$}