\(2018.2019.\left(\frac{2017}{2018}-\frac{2016}{2019}\right)\)
\(=2018.2019.\frac{2017}{2018}-2018.2019.\frac{2016}{2019}\)
\(=2019.2017-2018.2016\)
\(=\left(2018+1\right).\left(2016+1\right)-2018.2016\)
\(=\left(2018+1\right).2016+2018+1-2018.2016\)
\(=2018.2016+2016+2018+1-2018.2016\)
\(=2018.2016+4035-2016.2018\)
\(=4035\)
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