Đáp án:

$\begin{array}{l}
a)\frac{{23}}{{21}} > 1;\frac{{21}}{{23}} < 1\\
 \Rightarrow \frac{{23}}{{21}} > \frac{{21}}{{23}}\\
b)\frac{{ - 15}}{{ - 17}} = \frac{{15}}{{17}} > 0\\
\frac{{16}}{{ - 19}} < 0\\
 \Rightarrow \frac{{ - 15}}{{ - 17}} > \frac{{16}}{{ - 19}}\\
c)\frac{{19}}{{26}} = \frac{{19.25}}{{26.25}};\frac{{21}}{{25}} = \frac{{21.26}}{{25.26}}\\
Do:19.25 < 21.26\\
 \Rightarrow \frac{{19}}{{26}} < \frac{{21}}{{25}}\\
d)\frac{{ - 1999}}{{2000}} = \frac{{1 - 2000}}{{2000}} = \frac{1}{{2000}} - 1\\
\frac{{ - 2000}}{{2001}} = \frac{{1 - 2001}}{{2001}} = \frac{1}{{2001}} - 1\\
Do:\frac{1}{{2000}} > \frac{1}{{2001}}\\
 \Rightarrow \frac{{ - 1999}}{{2000}} > \frac{{ - 2000}}{{2001}}\\
e)\frac{{2019}}{{2020}} > \frac{{2019}}{{2020 + 2021}}\\
\frac{{2020}}{{2021}} > \frac{{2020}}{{2020 + 2021}}\\
 \Rightarrow \frac{{2019}}{{2020}} + \frac{{2020}}{{2021}} > \frac{{2019 + 2020}}{{2020 + 2021}}
\end{array}$