\(\dfrac{32}{3.7}+\dfrac{6}{7.41}+\dfrac{9}{41.10}+\dfrac{1}{51.10}+\dfrac{19}{51.14}\)
\(=\dfrac{32}{21}+\dfrac{6.5}{7.5.41}+\dfrac{9.5}{41.10.5}+\dfrac{5}{51.10.5}+\dfrac{19.5}{51.14.5}\)
\(=\dfrac{32}{21}+5.\left(\dfrac{6}{35.41}+\dfrac{9}{41.50}+\dfrac{1}{51.50}+\dfrac{19}{51.70}\right)\)
\(=\dfrac{32}{21}+5.\left(\dfrac{41-35}{35.41}+\dfrac{50-41}{41.50}+\dfrac{51-50}{51.50}+\dfrac{70-51}{51.70}\right)\)
\(=\dfrac{32}{21}+5.\left(\dfrac{1}{35}-\dfrac{1}{41}+\dfrac{1}{41}-\dfrac{1}{50}+\dfrac{1}{50}-\dfrac{1}{51}+\dfrac{1}{51}-\dfrac{1}{70}\right)\)
\(=\dfrac{32}{21}+5.\left(\dfrac{1}{35}-\dfrac{1}{70}\right)\)
\(=\dfrac{32}{21}+5.\dfrac{1}{70}\)
\(=\dfrac{32}{21}+\dfrac{1}{14}\)
\(=\dfrac{32.2}{42}+\dfrac{1.3}{42}\)
\(=\dfrac{67}{42}\)
