Thực hiện phép tính: \(\frac{{1000}}{{1009}} \cdot \frac{{ - 2018}}{{2019}} + \frac{{19}}{{2018}} \cdot \frac{{ - 2018}}{{2019}} + \frac{1}{{2020}}\)

* Hướng dẫn giải

\(\begin{array}{l}\,\,\,\,\frac{{1000}}{{1009}} \cdot \frac{{ - 2018}}{{2019}} + \frac{{19}}{{2018}} \cdot \frac{{ - 2018}}{{2019}} + \frac{1}{{2020}}\\ = \left( {\frac{{1000}}{{1009}} \cdot \frac{{ - 2018}}{{2019}} + \frac{{19}}{{2018}} \cdot \frac{{ - 2018}}{{2019}}} \right) + \frac{1}{{2020}}\\ = \frac{{ - 2018}}{{2019}} \cdot \left( {\frac{{1000}}{{1009}} + \frac{{19}}{{2018}}} \right) + \frac{1}{{2020}}\\ = \frac{{ - 2018}}{{2019}} \cdot \left( {\frac{{2000}}{{2018}} + \frac{{19}}{{2018}}} \right) + \frac{1}{{2020}}\\ = \frac{{ - 2018}}{{2019}} \cdot \frac{{2019}}{{2018}} + \frac{1}{{2020}}\\ =  - 1 + \frac{1}{{2020}}\\ = \frac{{ - 2020}}{{2020}} + \frac{1}{{2020}}\\ = \frac{{ - 2019}}{{2020}}\end{array}\)