\(\left(\frac{5}{4}-\frac{2}{5}\right)\times\frac{2017}{2018}+\left(\frac{3}{4}-\frac{3}{5}\right)\times\frac{2017}{2018}\)
\(=\left[\left(\frac{5}{4}-\frac{2}{5}\right)+\left(\frac{3}{4}-\frac{3}{5}\right)\right]\times\frac{2017}{2018}\)
\(=\left[\left(\frac{5}{4}+\frac{3}{4}\right)-\left(\frac{2}{5}+\frac{3}{5}\right)\right]\times\frac{2017}{2018}\)
\(=\left[2-1\right]\times\frac{2017}{2018}\)
\(=1\times\frac{2017}{2018}\)
\(=\frac{2017}{2018}\)
\(\left(\frac{5}{4}-\frac{2}{5}\right)\cdot\frac{2017}{2018}-\left(\frac{3}{4}-\frac{3}{5}\right)\cdot\frac{2017}{2018}\)
\(=\frac{2017}{2018}\cdot\left(\frac{5}{4}-\frac{2}{5}+\frac{3}{4}-\frac{3}{5}\right)\)
\(=\frac{2017}{2018}.\left(2+-1\right)\)
\(=\frac{2017}{2018}.1=\frac{2017}{2018}\)