the ________ of (a/b)^-1 is (a/b).
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Questioning whether (a + b)⁻¹ = a⁻¹ + b⁻¹ [with an implied “for all nonzero a and b such that b ≠ −a”, with the proscriptions being intended to prevent trying to deal with a reciprocal of 0] is just a special case of whether (a + b)ⁿ = aⁿ + bⁿ , namely n = −1.
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Reciprocal
The Reciprocal of a/b is b/a = (a/b)^-1
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