\(\dfrac{1}{4+\dfrac{1}{4+\dfrac{1}{4+\dfrac{1}{4}}}}\)
\(=\dfrac{1}{4+\dfrac{1}{4+\dfrac{1}{\dfrac{17}{4}}}}\)
\(=\dfrac{1}{4+\dfrac{1}{4+1\div\dfrac{17}{4}}}\)
\(=\dfrac{1}{4+\dfrac{1}{4+\dfrac{4}{17}}}\)
\(=\dfrac{1}{4+\dfrac{1}{\dfrac{72}{17}}}\)
\(=\dfrac{1}{4+\dfrac{17}{72}}\)
\(=\dfrac{1}{\dfrac{140}{17}}\)
\(=\dfrac{17}{40}\)
\(\dfrac{1}{4\dfrac{3}{7}}+\dfrac{1}{3\dfrac{11}{13}}+\dfrac{1}{\dfrac{5}{9}}\)
\(=\dfrac{1}{\dfrac{31}{7}}+\dfrac{1}{\dfrac{50}{13}}+\dfrac{1}{\dfrac{5}{9}}\)
\(=1\div\dfrac{31}{7}+1\div\dfrac{50}{13}+1\div\dfrac{5}{9}\)
\(=\dfrac{7}{31}+\dfrac{13}{50}+\dfrac{9}{5}\)
\(=\dfrac{3543}{1550}\)
