Bài giải:

$C=\frac{\left( 17\frac{1}{4}-4\frac{3}{16}-13\frac{5}{6} \right).\left( \frac{-4}{7} \right)+6\frac{3}{4}}{\left( 5\frac{2}{7}-\frac{16}{3} \right):\left( 6\frac{2}{3}-4\frac{1}{2} \right)}$

=$\frac{\left[ \left( 17-4-13 \right)+\left( \frac{1}{4}-\frac{3}{16}-\frac{5}{6} \right) \right].\left( \frac{-4}{7} \right)+\frac{27}{4}}{\left( \frac{37}{7}-\frac{16}{3} \right):\left( \frac{20}{3}-\frac{9}{2} \right)}$

=$\frac{\frac{-37}{48}.\frac{-4}{7}+\frac{27}{4}}{\frac{-1}{21}:\frac{13}{6}}$

=$\frac{\frac{37}{84}+\frac{27}{4}}{\frac{-1}{21}.\frac{6}{13}}$

=$\frac{\frac{151}{21}}{\frac{-2}{91}}$

=$\frac{-1963}{6}$