Question : The reciprocal of the sum of the reciprocals of $\frac{6}{5}$ and $\frac{3}{7}$ is:
Option 1: $\frac{57}{18}$
Option 2: $\frac{35}{57}$
Option 3: $\frac{6}{19}$
Option 4: $\frac{57}{35}$
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Correct Answer: $\frac{6}{19}$
Solution : Reciprocal of $\frac{6}{5}=\frac{5}{6}$ Reciprocal of $\frac{3}{7}=\frac{7}{3}$ Their sum = $(\frac{5}{6}+\frac{7}{3})=(\frac{5+14}{6} )=(\frac{19}{6} )$ Reciprocal of sum = $\frac{6}{19}$ Hence, the correct answer is $\frac{6}{19}$.
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