Bài 1:
a: \(\left(\dfrac{-3}{7}+\dfrac{4}{11}\right):\dfrac{7}{11}+\left(\dfrac{-4}{7}+\dfrac{7}{11}\right):\dfrac{7}{11}\)
\(=\left(-\dfrac{3}{7}+\dfrac{4}{11}+\dfrac{-4}{7}+\dfrac{7}{11}\right):\dfrac{7}{11}\)
\(=\left(-1+1\right)\cdot\dfrac{11}{7}=0\)
b: \(\dfrac{1}{99\cdot97}-\dfrac{1}{97\cdot95}-\dfrac{1}{95\cdot93}-...-\dfrac{1}{5\cdot3}-\dfrac{1}{3\cdot1}\)
\(=\dfrac{1}{99\cdot97}-\left(\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{93\cdot95}+\dfrac{1}{95\cdot97}\right)\)
\(=\dfrac{1}{97\cdot99}-\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{93\cdot95}+\dfrac{2}{95\cdot97}\right)\)
\(=\dfrac{1}{97\cdot99}-\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{95}-\dfrac{1}{97}\right)\)
\(=\dfrac{1}{97\cdot99}-\dfrac{1}{2}\left(1-\dfrac{1}{97}\right)\)
\(=\dfrac{1}{97\cdot99}-\dfrac{48}{97}=\dfrac{1-48\cdot99}{99\cdot97}=\dfrac{-4751}{99\cdot97}=\dfrac{-4751}{9603}\)
