Cho [M = left( { frac{{21}}{{31}} + frac{{ - 16}}{7}} right) + left( { frac{{44}}{{53}} + frac{{10}}{{31}}} right) + frac{9}{{53}} ] và [N = frac{1}{2} + frac{{ - 1}}{5} + frac{{

* Hướng dẫn giải

\[M = \left( {\frac{{21}}{{31}} + \frac{{ - 16}}{7}} \right) + \left( {\frac{{44}}{{53}} + \frac{{10}}{{31}}} \right) + \frac{9}{{53}}\]

\[M = \frac{{21}}{{31}} + \frac{{ - 16}}{7} + \frac{{44}}{{53}} + \frac{{10}}{{31}} + \frac{9}{{53}}\]

\[M = \left( {\frac{{21}}{{31}} + \frac{{10}}{{31}}} \right) + \left( {\frac{{44}}{{53}} + \frac{9}{{53}}} \right) + \frac{{ - 16}}{7}\]

\[M = 1 + 1 + \frac{{ - 16}}{7}\]

\[M = 2 + \frac{{ - 16}}{7}\]

\[M = \frac{{ - 2}}{7}\]

\[N = \frac{1}{2} + \frac{{ - 1}}{5} + \frac{{ - 5}}{7} + \frac{1}{6} + \frac{{ - 3}}{{35}} + \frac{1}{3} + \frac{1}{{41}}\]

\[N = \left( {\frac{1}{2} + \frac{1}{6} + \frac{1}{3}} \right) + \left( {\frac{{ - 1}}{5} + \frac{{ - 5}}{7} + \frac{{ - 3}}{{35}}} \right) + \frac{1}{{41}}\]

\[N = \frac{{3 + 1 + 2}}{6} + \frac{{\left( { - 7} \right) + \left( { - 25} \right) + \left( { - 3} \right)}}{{35}} + \frac{1}{{41}}\]

\[\begin{array}{l}N = 1 + \left( { - 1} \right) + \frac{1}{{41}}\\N = \frac{1}{{41}}\end{array}\]

Đáp án cần chọn là: D