Решение и ответ:

[tex]\displaystyle 2\frac{3}{7}+\left({-3\frac{1}{2}}\right)-5\frac{9}{{14}}=-6\frac{5}{7}[/tex]

[tex]\displaystyle 2\frac{3}{7}+\left({-3\frac{1}{2}}\right)=2\frac{3}{7}-3\frac{1}{2}=2\frac{6}{{14}}-3\frac{7}{{14}}=-1\frac{1}{{14}}[/tex]

[tex]\displaystyle -1\frac{1}{{14}}-5\frac{9}{{14}}=-\left({1\frac{1}{{14}}+5\frac{9}{{14}}}\right)=-6\frac{{10}}{{14}}=-6\frac{5}{7}[/tex]