Đáp án:

$\begin{array}{l}
12)b)\\
\dfrac{{10}}{{13}} < \dfrac{7}{a} < \dfrac{{10}}{{11}}\\
 \Rightarrow \dfrac{{70}}{{13.7}} < \dfrac{{7.10}}{{a.10}} < \dfrac{{70}}{{11.7}}\\
 \Rightarrow \dfrac{{70}}{{91}} < \dfrac{{70}}{{10.a}} < \dfrac{{70}}{{77}}\\
 \Rightarrow 77 < 10.a < 91\\
 \Rightarrow \left\{ \begin{array}{l}
10.a = 80\\
10.a = 90
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
a = 8\\
a = 9
\end{array} \right.\\
 \Rightarrow Phân\,số:\dfrac{7}{8};\dfrac{7}{9}\\
c)Mẫu:a;a + 1\\
 \Rightarrow \dfrac{8}{a};\dfrac{8}{{a + 1}}\\
Do:\dfrac{8}{a} > \dfrac{8}{{a + 1}}\\
 \Rightarrow \dfrac{8}{{a + 1}} < \dfrac{5}{7} < \dfrac{8}{a}\\
 \Rightarrow \dfrac{{40}}{{5.\left( {a + 1} \right)}} < \dfrac{{40}}{{56}} < \dfrac{{40}}{{5a}}\\
 \Rightarrow 5a < 56 < 5\left( {a + 1} \right)\\
 \Rightarrow 5a < 56 < 5a + 5\\
 \Rightarrow a = 11\\
 \Rightarrow Phân\,số:\dfrac{8}{{11}};\dfrac{8}{{12}}\\
13)b)y = \dfrac{{a + 2}}{{a - 1}} = \dfrac{{a - 1 + 3}}{{a - 1}}\\
 = 1 + \dfrac{3}{{a - 1}}\\
y \in Z\\
 \Rightarrow \dfrac{3}{{a - 1}} \in Z\\
 \Rightarrow \left( {a - 1} \right) \in Ư\left( 3 \right) = \left\{ { - 3; - 1;1;3} \right\}\\
 \Rightarrow a \in \left\{ { - 2;0;2;4} \right\}\left( {tmdk} \right)\\
c)z = \dfrac{{2a - 5}}{{a + 1}}\\
 = \dfrac{{2a + 2 - 7}}{{a + 1}} = \dfrac{{2\left( {a + 1} \right) - 7}}{{a + 1}}\\
 = 2 - \dfrac{7}{{a + 1}}\\
z \in Z\\
 \Rightarrow \dfrac{7}{{a + 1}} \in Z\\
 \Rightarrow \left( {a + 1} \right) \in Ư\left( 7 \right) = \left\{ { - 7; - 1;1;7} \right\}\\
 \Rightarrow a \in \left\{ { - 8; - 2;0;6} \right\}\left( {tmdk} \right)
\end{array}$