Đáp án:
+)Để A có giá trị nguyên thì 3 chia hết cho (x-1)
$\begin{array}{l}
\Rightarrow \left( {x - 1} \right) \in Ư\left( 3 \right) = \left\{ { - 3; - 1;1;3} \right\}\\
\Rightarrow x \in \left\{ { - 2;0;2;4} \right\}\\
+ )B = \dfrac{{3x + 7}}{{x - 1}} = \dfrac{{3\left( {x - 1} \right) + 3 + 7}}{{x - 1}} = 3 + \dfrac{{10}}{{x - 1}}\\
B \in Z\\
\Rightarrow \dfrac{{10}}{{x - 1}} \in Z\\
\Rightarrow 10 \vdots \left( {x - 1} \right)\\
\Rightarrow \left( {x - 1} \right) \in Ư\left( {10} \right)\\
\Rightarrow \left( {x - 1} \right) \in \left\{ { - 10; - 5; - 2; - 1;1;2;5;10} \right\}\\
\Rightarrow x \in \left\{ { - 9; - 4; - 1;0;2;3;6;11} \right\}
\end{array}$
