Bài 1 :
a) \(\dfrac{2}{15}+\dfrac{5}{9}+\dfrac{-2}{3}=\dfrac{31}{45}+\dfrac{-2}{3}=\dfrac{1}{45}\)
b) \(\dfrac{-3}{31}+\dfrac{6}{17}-\dfrac{-1}{25}+\dfrac{-28}{31}+\dfrac{11}{17}-\dfrac{1}{5}\)
\(=\dfrac{-3}{31}+\dfrac{6}{17}+\dfrac{1}{25}+\dfrac{-28}{31}+\dfrac{11}{17}-\dfrac{1}{5}\)
\(=\left(\dfrac{-3}{31}+\dfrac{-28}{31}\right)+\left(\dfrac{6}{17}+\dfrac{11}{17}\right)+\left(\dfrac{1}{25}-\dfrac{1}{5}\right)\)
\(=-\dfrac{31}{31}+\dfrac{17}{17}+\dfrac{-4}{25}\)
\(=\left(-1\right)+1+\dfrac{-4}{25}\)
\(=-\dfrac{4}{25}\)
Bài 2
a) \(x+\dfrac{7}{8}=\dfrac{13}{12}\)
\(x=\dfrac{13}{12}-\dfrac{7}{8}\)
\(x=\dfrac{5}{24}\)
b) \(3\dfrac{2}{3}\cdot x+5\dfrac{1}{2}=11\dfrac{1}{6}\)
\(\dfrac{11}{3}\cdot x+\dfrac{11}{2}=\dfrac{67}{6}\)
\(\dfrac{11}{3}\cdot x=\dfrac{67}{6}-\dfrac{11}{2}\)
\(\dfrac{11}{3}\cdot x=\dfrac{17}{3}\)
\(x=\dfrac{17}{3}\div\dfrac{11}{3}\)
\(x=\dfrac{17}{11}\)
Bài 3
\(S=\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}\)
\(S=\cdot\left(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}\right)\)
\(S=\left(\dfrac{1}{1}-\dfrac{1}{16}\right)\)
\(S=\dfrac{15}{16}\)
