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algebra intermediate

Problem

When simplified,

(x^{- 1} + y^{- 1})^{- 1}

is equal to:

(A)

x + y

(B)

\frac{x y}{x + y}

(C)

x y

(D)

\frac{1}{x y}

Solution

(x^{- 1} + y^{- 1})^{- 1} = (\frac{1}{x} + \frac{1}{y})^{- 1} = (\frac{x + y}{x y})^{- 1} = \frac{x y}{x + y}

.

Final answer

B