Ta có: \(\frac{15}{6\cdot16}+\frac{15}{16\cdot26}+\frac{15}{26\cdot36}\)
\(=\frac{15}{10}\cdot\left(\frac{10}{6\cdot16}+\frac{10}{16\cdot26}+\frac{10}{26\cdot36}\right)\)
\(=\frac32\left(\frac16-\frac{1}{16}+\frac{1}{16}-\frac{1}{26}+\frac{1}{26}-\frac{1}{36}\right)\)
\(=\frac32\left(\frac16-\frac{1}{36}\right)=\frac32\cdot\frac{5}{36}=\frac{15}{72}=\frac{5}{24}\)
Ta có: \(\frac{33}{6\cdot16}-\frac{63}{16\cdot26}+\frac{93}{26\cdot36}\)
\(=\frac32\left(\frac{22}{6\cdot16}-\frac{42}{16\cdot26}+\frac{63}{26\cdot36}\right)\)
\(=\frac32\left(\frac16+\frac{1}{16}-\frac{1}{16}-\frac{1}{26}+\frac{1}{26}+\frac{1}{36}\right)\)
\(=\frac32\left(\frac16+\frac{1}{36}\right)=\frac32\cdot\frac{7}{36}=\frac{7}{12\cdot2}=\frac{7}{24}\)
Ta có: \(A=\frac{\frac{15}{6\cdot16}+\frac{15}{16\cdot26}+\frac{15}{26\cdot36}}{\frac{33}{6\cdot16}-\frac{63}{16\cdot26}+\frac{93}{26\cdot36}}\)
\(=\frac{5}{24}:\frac{7}{24}=\frac57\)
