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1977 AMC 12 Question 6

AMC12 · 1977 AMC 12

Question 6

If $x,$ $y$ and $2x+\frac y2$ are not zero, then $$
\left(2x+\frac y2\right)^{-1}\left[(2x)^{-1}+\left(\frac y2\right)^{-1}\right]
$$ equals
  1. $1$
  2. $xy^{-1}$
  3. $x^{-1}y$
  4. $(xy)^{-1}$
  5. none of these