Cho \(D = \frac{5}{{6.37}} + \frac{1}{{6.43}} + \frac{6}{{7.43}} + \frac{{10}}{{7.59}}\) và \(E = \frac{8}{{9.37}} + \frac{2}{{9.47}} + \frac{3}{{10.47}} + \frac{9}{{10.59}}\). Tính \(\frac{D}{E}\)?

\(D = \frac{5}{{6.37}} + \frac{1}{{6.43}} + \frac{6}{{7.43}} + \frac{{10}}{{7.59}}\)

\(\frac{1}{7}D = \frac{5}{{37.42}} + \frac{1}{{42.43}} + \frac{6}{{43.49}} + \frac{{10}}{{49.59}}\)

\(\frac{1}{7}D = \frac{1}{{37}} - \frac{1}{{42}} + \frac{1}{{42}} - \frac{1}{{43}} + \frac{1}{{43}} - \frac{1}{{49}} + \frac{1}{{49}} - \frac{1}{{59}}\)

\(\frac{1}{7}D = \frac{1}{{37}} - \frac{1}{{59}}\)

\(D = 7\left( {\frac{1}{{37}} - \frac{1}{{59}}} \right)\)

\(E = \frac{8}{{9.37}} + \frac{2}{{9.47}} + \frac{3}{{10.47}} + \frac{9}{{10.59}}\)

\(\frac{1}{5}E = \frac{8}{{37.45}} + \frac{2}{{45.47}} + \frac{3}{{47.50}} + \frac{9}{{50.59}}\)

\(\frac{1}{5}E = \frac{1}{{37}} - \frac{1}{{45}} + \frac{1}{{45}} - \frac{1}{{47}} + \frac{1}{{47}} - \frac{1}{{50}} + \frac{1}{{50}} - \frac{1}{{59}}\)

\(\frac{1}{5}E = \frac{1}{{37}} - \frac{1}{{59}}\)

\(E = 5\left( {\frac{1}{{37}} - \frac{1}{{59}}} \right)\)

Suy ra: \(\frac{D}{E} = \frac{{7\left( {\frac{1}{{37}} - \frac{1}{{59}}} \right)}}{{5\left( {\frac{1}{{37}} - \frac{1}{{59}}} \right)}} = \frac{7}{5}\).