\(\left(\frac{151515}{161616}+\frac{17^9}{17^{10}}\right)-\left(\frac{1500}{1600}-\frac{1616}{1717}\right)\)
\(=\left(\frac{15.10101}{16.10101}+\frac{1}{17}\right)-\left(\frac{15.100}{16.100}-\frac{16.101}{17.101}\right)\)
\(=\frac{15}{16}+\frac{1}{17}-\frac{15}{16}+\frac{16}{17}=\frac{1}{17}+\frac{16}{17}=\frac{17}{17}=1\)
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