\(A=\left[\left(\dfrac{-3}{5}+\dfrac{4}{9}\right):\dfrac{2}{7}-\left(\dfrac{-14}{9}+\dfrac{2}{5}\right):\dfrac{2}{7}\right]:\left(3\dfrac{2}{7}.7\dfrac{1}{2}-3\dfrac{2}{7}.5\dfrac{1}{2}\right).\)
\(=\left(\dfrac{-3}{5}+\dfrac{4}{9}:\dfrac{2}{7}-\dfrac{-14}{9}+\dfrac{2}{5}:\dfrac{2}{7}\right):\left(\dfrac{23}{7}.\dfrac{15}{2}-\dfrac{23}{7}.\dfrac{11}{2}\right).\)
\(=\left[\left(\dfrac{-3}{5}+\dfrac{2}{5}\right)-\left(\dfrac{4}{9}-\dfrac{-14}{9}\right):\dfrac{2}{7}\right]:\left[\dfrac{23}{7}.\left(\dfrac{15}{2}:\dfrac{11}{2}\right)\right].\)
\(=\left[\left(\dfrac{-1}{5}-\dfrac{16}{9}\right):\dfrac{2}{7}\right]:\left[\dfrac{23}{7}.\left(\dfrac{15}{2}+\dfrac{-11}{2}\right)\right].\)
\(=\left[\left(\dfrac{-1}{5}+\dfrac{-16}{9}\right):\dfrac{2}{7}\right]:\left(\dfrac{-4}{2}.\dfrac{23}{7}\right).\)
\(=\left[\left(\dfrac{-9}{45}+\dfrac{-90}{45}\right):\dfrac{2}{7}\right]:\left(-2.\dfrac{23}{7}\right).\)
\(=\left(\dfrac{-99}{45}:\dfrac{2}{7}\right):\dfrac{-46}{7}.\)
\(=\left(\dfrac{-11}{5}:\dfrac{2}{7}\right):\dfrac{-46}{7}.\)
\(=\dfrac{-77}{10}:\dfrac{-46}{7}.\)
\(=\dfrac{539}{460}.\)
\(B=\left(1-\dfrac{2}{2.3}\right)\left(1-\dfrac{2}{3.4}\right)\left(1-\dfrac{2}{4.5}\right)...\left(1-\dfrac{2}{99.100}\right).\)
\(=\left(\dfrac{6}{2.3}-\dfrac{2}{2.3}\right)\left(\dfrac{12}{3.4}-\dfrac{2}{3.4}\right)\left(\dfrac{20}{4.5}-\dfrac{2}{4.5}\right)...\left(\dfrac{9900}{99.100}-\dfrac{2}{99.100}\right).\)
\(=\dfrac{4}{2.3}.\dfrac{10}{3.4}.\dfrac{18}{4.5}...\dfrac{9898}{99.100}.\)
\(=\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}...\dfrac{98.101}{99.100}.\)
\(=\dfrac{1.2.3....98}{2.3...99}.\dfrac{4.5.6...101}{3.4.100}.\)
\(=\dfrac{1}{99}.\dfrac{101}{3}.\)
\(=\dfrac{101}{297}.\)
Giúp em với ạ, em cần gấp trước 7h15 ạ. Em cảm ơn nhiều.
