Ta có :
\(A=\dfrac{34}{7.13}+\dfrac{51}{13.22}+\dfrac{85}{22.37}+\dfrac{68}{37.49}\)
\(\dfrac{A}{17}=\dfrac{2}{7.13}+\dfrac{3}{13.22}+\dfrac{5}{22.37}+\dfrac{4}{37.49}\)
\(A.\dfrac{3}{17}=\dfrac{6}{7.13}+\dfrac{9}{13.22}+\dfrac{15}{22.37}+\dfrac{12}{37.49}\)
\(A.\dfrac{3}{17}=\dfrac{1}{7}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{22}+\dfrac{1}{22}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{49}\)
\(A.\dfrac{3}{17}=\dfrac{1}{7}-\dfrac{1}{49}\)
\(A.\dfrac{3}{17}=\dfrac{6}{49}\)
\(\Rightarrow A=\dfrac{6}{49}:\dfrac{3}{17}=\dfrac{34}{49}\)
\(B=\dfrac{39}{7.16}+\dfrac{65}{16.31}+\dfrac{52}{31.43}+\dfrac{26}{37.49}\)
\(\dfrac{B}{13}=\dfrac{3}{7.16}+\dfrac{5}{16.31}+\dfrac{4}{31.43}+\dfrac{2}{37.49}\)
\(B.\dfrac{3}{13}=\dfrac{9}{7.16}+\dfrac{15}{16.31}+\dfrac{12}{31.43}+\dfrac{6}{43.49}\)
\(B.\dfrac{3}{13}=\dfrac{1}{7}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{43}+\dfrac{1}{43}-\dfrac{1}{49}\)
\(B.\dfrac{3}{13}=\dfrac{1}{7}-\dfrac{1}{49}\)
\(B.\dfrac{3}{13}=\dfrac{1}{7}-\dfrac{1}{49}=\dfrac{6}{49}\)
\(\Rightarrow B=\dfrac{6}{49}:\dfrac{3}{13}=\dfrac{26}{49}\)
\(\Rightarrow\dfrac{A}{B}=\dfrac{34}{49}:\dfrac{26}{49}=\dfrac{17}{13}\)
Chúc bn học tốt!!!!!!!!!