Discussion
The average of reciprocals of a and b is :
Answer: B
The average is \(\frac{a+b}{2ab}\).
The reciprocals are \(\frac{1}{a}\) and \(\frac{1}{b}\). Their average is half their sum:
\[ \begin{aligned} \tfrac{1}{2}\left(\tfrac{1}{a} + \tfrac{1}{b}\right) &= \tfrac{1}{2} \cdot \tfrac{a+b}{ab} \\ &= \tfrac{a+b}{2ab} \end{aligned} \]
\(\frac{2(a+b)}{ab}\) multiplies by 2 instead of dividing. \(\frac{2ab}{a+b}\) is the reciprocal of the answer, the harmonic mean of a and b. \(\frac{a+b}{a-b}\) has no connection with the average.
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