giúp e luôn với ạ
\(a,\dfrac{7}{4}+\dfrac{-5}{7}-\dfrac{11}{-14}\)
\(=\dfrac{7}{4}+\dfrac{-5}{7}+\dfrac{11}{14}\)
\(=\dfrac{7}{4}+\left(\dfrac{-5}{7}+\dfrac{11}{14}\right)\)
\(=\dfrac{7}{4}+\dfrac{1}{14}\)
\(=\dfrac{51}{28}\)
\(b,\left(\dfrac{5}{9}+2\dfrac{5}{11}\right)+\left(1\dfrac{4}{9}-1\dfrac{5}{11}\right)\)
\(=\left(\dfrac{5}{9}+\dfrac{27}{11}\right)+\left(\dfrac{13}{9}-\dfrac{16}{11}\right)\)
\(=\dfrac{5}{9}+\dfrac{27}{11}+\dfrac{13}{9}-\dfrac{16}{11}\)
\(=\left(\dfrac{5}{9}+\dfrac{13}{9}\right)+\left(\dfrac{27}{11}-\dfrac{16}{11}\right)\)
\(=2+1=3\)
\(c,\dfrac{7}{6}+\dfrac{5}{6}.\dfrac{11}{13}-\dfrac{5}{13}:\dfrac{6}{25}\)
\(=\dfrac{7}{6}+\dfrac{11}{6}.\dfrac{5}{13}-\dfrac{5}{13}.\dfrac{25}{6}\)
\(=\dfrac{7}{6}+\dfrac{5}{13}.\left(\dfrac{11}{6}-\dfrac{25}{6}\right)\)
\(=\dfrac{7}{6}+\dfrac{5}{13}.-\dfrac{7}{3}\)
\(=\dfrac{7}{6}+-\dfrac{35}{39}\)
\(=\dfrac{7}{26}\)
d) \(\dfrac{3^3}{1.3}+\dfrac{3^3}{3.5}+\dfrac{3^3}{5.7}+...+\dfrac{3^3}{97.99}\)
2A = \(3^3.\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\right)\)
2A = \(27.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
2A = \(27.\left(1-\dfrac{1}{99}\right)\)
2A = \(27.\left(\dfrac{99}{99}-\dfrac{1}{99}\right)\)
2A = \(27.\dfrac{98}{99}\)
2A = \(\dfrac{294}{11}\)
A = \(\dfrac{294}{11}:2\)
A = \(\dfrac{294}{11}.\dfrac{1}{2}\)
A = \(\dfrac{147}{11}\)
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