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2015 AMC 10BProblem 7P1-10~2 minPrint
FunctionsFractions & DecimalsSet up the equation/formula and compute; no special trick needed

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)) ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.