For nonzero x and y with x + y ≠ 0, which expression is equal to (x⁻¹ + y⁻¹)⁻¹?

Question

Accepted Answer

A. xy/(x + y). x⁻¹ + y⁻¹ = 1/x + 1/y = (x + y)/(xy). Its reciprocal is xy/(x + y).

Answer

B. x + y — The reciprocal of a sum is not the sum of the reciprocals; (x⁻¹ + y⁻¹)⁻¹ ≠ x + y.

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C. (x + y)/(xy) — (x + y)/(xy) is x⁻¹ + y⁻¹ itself, before taking the reciprocal.

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D. 1/(x + y) — 1/(x + y) ignores the xy numerator.

Advanced Math practice question