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\(A=\frac{34}{7.13}+\frac{51}{13.22}+\frac{85}{22.37}+\frac{68}{37.49}\)
\(=17.\left(\frac{2}{7.13}+\frac{3}{13.22}+\frac{5}{22.37}+\frac{4}{37.49}\right)\)
\(=\frac{17}{3}.\left(\frac{6}{7.13}+\frac{9}{13.22}+\frac{15}{22.37}+\frac{12}{37.49}\right)\)
\(=\frac{17}{3}\left(\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{22}+\frac{1}{22}-\frac{1}{37}+\frac{1}{37}-\frac{1}{49}\right)\)
\(=\frac{17}{3}\left(\frac{1}{7}-\frac{1}{49}\right)\)
\(B=\frac{39}{7.16}+\frac{65}{16.31}+\frac{52}{31.43}+\frac{26}{43.49}\)
\(=13\left(\frac{3}{7.16}+\frac{5}{16.31}+\frac{4}{31.43}+\frac{2}{43.49}\right)\)
\(=\frac{13}{3}\left(\frac{9}{7.16}+\frac{15}{16.31}+\frac{12}{31.43}+\frac{6}{43.49}\right)\)
\(=\frac{13}{3}\left(\frac{1}{7}-\frac{1}{16}+\frac{1}{16}-\frac{1}{31}+\frac{1}{31}-\frac{1}{43}+\frac{1}{43}-\frac{1}{49}\right)\)
\(=\frac{13}{3}\left(\frac{1}{7}-\frac{1}{49}\right)\)
\(\Rightarrow\frac{A}{B}=\frac{\frac{17}{3}\left(\frac{1}{7}-\frac{1}{49}\right)}{\frac{13}{3}\left(\frac{1}{7}-\frac{1}{49}\right)}=\frac{\frac{17}{3}}{\frac{13}{3}}=\frac{17}{13}\)
Sửa đề: \(A=\dfrac{34}{7\cdot13}+\dfrac{51}{13\cdot22}+\dfrac{85}{22\cdot37}+\dfrac{68}{37\cdot49}\)
\(=17\left(\dfrac{2}{7\cdot13}+\dfrac{3}{13\cdot22}+\dfrac{5}{22\cdot37}+\dfrac{4}{37\cdot49}\right)\)
\(=\dfrac{17}{3}\left(\dfrac{6}{7\cdot13}+\dfrac{9}{13\cdot22}+\dfrac{15}{22\cdot37}+\dfrac{12}{37\cdot49}\right)\)
\(=\dfrac{17}{3}\left(\dfrac{1}{7}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{22}+\dfrac{1}{22}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{49}\right)\)
\(=\dfrac{17}{3}\left(\dfrac{1}{7}-\dfrac{1}{49}\right)\)
\(B=\dfrac{39}{7\cdot16}+\dfrac{65}{16\cdot31}+\dfrac{52}{31\cdot43}+\dfrac{26}{43\cdot49}\)
\(=13\left(\dfrac{3}{7\cdot16}+\dfrac{5}{16\cdot31}+\dfrac{4}{31\cdot43}+\dfrac{2}{43\cdot49}\right)\)
\(=\dfrac{13}{3}\left(\dfrac{9}{7\cdot16}+\dfrac{15}{16\cdot31}+\dfrac{12}{31\cdot43}+\dfrac{6}{43\cdot49}\right)\)
\(=\dfrac{13}{3}\left(\dfrac{1}{7}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{43}+\dfrac{1}{43}-\dfrac{1}{49}\right)\)
\(=\dfrac{13}{3}\left(\dfrac{1}{7}-\dfrac{1}{49}\right)\)
\(\dfrac{A}{B}=\dfrac{\dfrac{17}{3}\left(\dfrac{1}{7}-\dfrac{1}{49}\right)}{\dfrac{13}{3}\left(\dfrac{1}{7}-\dfrac{1}{49}\right)}=\dfrac{17}{3}:\dfrac{13}{3}=\dfrac{17}{13}\)