a: \(\left(17\frac{21}{56}-13\frac{21}{45}\right):\left(\frac34+\frac{11}{30}\right)\)
\(=\left(17+\frac37-13-\frac{7}{15}\right):\left(\frac{45}{60}+\frac{22}{60}\right)\)
\(=\left(4+\frac37-\frac{7}{15}\right):\frac{67}{60}=\frac{420+45-49}{105}\cdot\frac{60}{67}=\frac{416}{67}\cdot\frac{60}{105}=\frac{416}{67}\cdot\frac47\)
\(=\frac{1664}{67\cdot7}\)
\(A=\frac{\left(17\frac{21}{56}-13\frac{21}{45}\right):\left(\frac34+\frac{11}{30}\right)}{9^3\cdot100-2\cdot3^2}\)
\(=\frac{1664}{67\cdot7}:\left(3^6\cdot2^2\cdot5^2-2\cdot3^2\right)=\frac{1664}{67\cdot7\cdot2\cdot3^2\left(3^4\cdot2\cdot5^2-1\right)}=\frac{832}{67\cdot7\cdot3^2\cdot4049}\)
c: \(C=5\frac{9}{10}:\frac32-\left(2\frac13\cdot4\frac12-2-2\frac12\right):\frac74\)
\(=\frac{59}{10}\cdot\frac23-\left(\frac73\cdot\frac92-2-\frac52\right)\cdot\frac47\)
\(=\frac{59}{15}-\left(\frac{21}{2}-\frac52-2\right)\cdot\frac47=\frac{59}{15}-7\cdot\frac47=\frac{59}{15}-4=-\frac{1}{15}\)
