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Minus the Reciprocal of Function

Source: 2015 amc 10b #7

February 26, 2015
functionAMC

Problem Statement

Consider the operation "minus the reciprocal of," defined by a⋄b=a−1ba\diamond b=a-\frac{1}{b}. What is ((1⋄2)⋄3)−(1⋄(2⋄3))((1\diamond2)\diamond3)-(1\diamond(2\diamond3))? <spanclass=′latex−bold′>(A)</span>−730<spanclass=′latex−bold′>(B)</span>−16<spanclass=′latex−bold′>(C)</span>0<spanclass=′latex−bold′>(D)</span>16<spanclass=′latex−bold′>(E)</span>730<span class='latex-bold'>(A) </span> -\dfrac{7}{30} \qquad<span class='latex-bold'>(B) </span> -\dfrac{1}{6} \qquad<span class='latex-bold'>(C) </span> 0 \qquad<span class='latex-bold'>(D) </span> \dfrac{1}{6} \qquad<span class='latex-bold'>(E) </span> \dfrac{7}{30}
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