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A=\(\frac{2}{1}\cdot3+\frac{2}{3}\cdot5+\frac{2}{5}\cdot7+\frac{2}{7}\cdot9\)
A=\(\frac{3}{1}\cdot2+\frac{5}{3}\cdot2+\frac{7}{5}\cdot2+\frac{9}{7}\cdot2\)
A=\(2\cdot\left(3+\frac{5}{3}+\frac{7}{5}+\frac{9}{7}\right)\)
A=\(2\cdot\frac{772}{105}\)
A=\(\frac{1544}{105}\)
A=\(14\frac{74}{105}\)
\(\frac{2}{7}+\frac{1}{4}+\frac{5}{7}+\frac{3}{4}\)
\(=\)
\(\left(\frac{2}{7}+\frac{5}{7}\right)+\)\(\left(\frac{1}{4}+\frac{3}{4}\right)\)
\(=1+1\)
\(=2\)
\(\frac{2}{7}+\frac{1}{4}+\frac{5}{7}+\frac{3}{4}\)
\(=\left(\frac{2}{7}+\frac{5}{7}\right)+\left(\frac{1}{4}+\frac{3}{4}\right)\)
\(=1+1\)
\(=2.\)
\(A=\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+.......+\frac{2}{99.101}\right)\)
\(=\frac{7}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+......+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\left(1-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\frac{100}{101}\)
\(=\frac{350}{101}\)
\(A=\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+.....+\frac{2}{99.101}\right)\)
\(=\frac{7}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-.....+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\left(1-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\frac{100}{101}\)
\(=\frac{350}{101}\)
\(\frac{\frac{6}{5}-\frac{2}{5}}{\frac{5x3}{7}-\frac{3x3}{7}}\)
\(=\frac{\frac{4}{5}}{\frac{5x3-3x3}{7}}\)
\(=\frac{\frac{4}{5}}{\frac{6}{7}}=\frac{4}{5}:\frac{6}{7}\)
\(=\frac{14}{15}\)
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