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2015 AMC 10B Question 7

AMC10 · 2015 AMC 10B

Question 7

Consider the operation “minus the reciprocal of,” defined by $a\diamond b=a-\frac{1}{b}.$ What is $$
((1\diamond2)\diamond3)-(1\diamond(2\diamond3))?
$$
  1. $ -\dfrac{7}{30} $
  2. $ -\dfrac{1}{6} $
  3. $ 0 $
  4. $ \dfrac{1}{6} $
  5. $ \dfrac{7}{30} $