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4

Part of 2012 Math Prize For Girls Problems

Problems(1)

Math Prize 2012 Problem 4

Source:

9/24/2012
Evaluate the expression 121(113−117)+169(117−111)+289(111−113)11(113−117)+13(117−111)+17(111−113) . \frac{121 \left( \frac{1}{13} - \frac{1}{17} \right) + 169 \left( \frac{1}{17} - \frac{1}{11} \right) + 289 \left( \frac{1}{11} - \frac{1}{13} \right)}{ 11 \left( \frac{1}{13} - \frac{1}{17} \right) + 13 \left( \frac{1}{17} - \frac{1}{11} \right) + 17 \left( \frac{1}{11} - \frac{1}{13} \right)} \, .