Question

If \( H \) is the harmonic mean between \( P \) and \( Q \), then the value of \[ \frac{H}{P} + \frac{H}{Q} \] is

• A. \( \frac{PQ}{P + Q} \)
• B. \( \frac{P + Q}{PQ} \)
• C. \( \frac{1}{2} \)
• D. \( 2 \)

Hint:

The harmonic mean is related to the arithmetic mean and the geometric mean. Use the formula \( H = \frac{2PQ}{P + Q} \) for solving related problems.

Answer 1

The Correct Option is B

Step 1: Formula for harmonic mean.
The harmonic mean is given by \( H = \frac{2PQ}{P + Q} \). Using this formula, we can simplify the expression \( \frac{H}{P} + \frac{H}{Q} \).

Step 2: Conclusion.
Thus, the correct answer is option (B).

Final Answer: \[ \boxed{\text{(B) } \frac{P + Q}{PQ}} \]