Advanced MathVery hardInverting a sum of reciprocals
Advanced Math practice question
For positive x and y, which expression is equivalent to (x⁻¹ + y⁻¹)⁻¹?
- A. xy/(x + y)Correct
- B. x + y
- C. (x + y)/(xy)
- D. 1/(xy)
Answer: A. xy/(x + y)
x⁻¹ + y⁻¹ = (x + y)/(xy), and its reciprocal is xy/(x + y).
Why the other answers are wrong
- B. x + y
- The reciprocal of a sum is not the sum of reciprocals.
- C. (x + y)/(xy)
- This is x⁻¹ + y⁻¹ before the final inversion.
- D. 1/(xy)
- This inverts the product only.
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