1:
a: \(A=3\dfrac{1}{10}:\left[4\cdot\left(-3\right)^2-2^3:\dfrac{8}{5}\right]\)
\(=3,1:\left[4\cdot9-8\cdot\dfrac{5}{8}\right]\)
\(=3,1:\left(36-5\right)=3,1:31=0,1\)
b: \(B=\left(1\dfrac{1}{3}\right)\left(1\dfrac{1}{8}\right)\left(1\dfrac{1}{15}\right)\cdot...\cdot\left(1\dfrac{1}{99}\right)\)
\(=\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot\dfrac{16}{15}\cdot...\cdot\dfrac{100}{99}\)
\(=\dfrac{2\cdot2}{1\cdot3}\cdot\dfrac{3\cdot3}{2\cdot4}\cdot\dfrac{4\cdot4}{3\cdot5}\cdot...\cdot\dfrac{10\cdot10}{9\cdot11}\)
\(=\dfrac{2\cdot3\cdot4\cdot...\cdot10}{1\cdot2\cdot3\cdot...\cdot9}\cdot\dfrac{2\cdot3\cdot...\cdot10}{3\cdot4\cdot5\cdot...\cdot11}\)
\(=\dfrac{10}{1}\cdot\dfrac{2}{11}=\dfrac{20}{11}\)
2: \(C=\dfrac{5}{2\cdot7}+\dfrac{16}{7\cdot9}-\dfrac{2}{9\cdot11}-\dfrac{29}{11\cdot18}\)
\(=\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{9}-\left(\dfrac{1}{9}-\dfrac{1}{11}\right)-\dfrac{1}{11}-\dfrac{1}{18}\)
\(=\dfrac{1}{2}+\dfrac{1}{9}-\dfrac{1}{9}+\dfrac{1}{11}-\dfrac{1}{11}-\dfrac{1}{18}=\dfrac{1}{2}-\dfrac{1}{18}\)
\(=\dfrac{8}{18}=\dfrac{4}{9}\)
