\(a,A=\dfrac{2x^2-6x+x^2+3x-3+11x}{\left(x-3\right)\left(x+3\right)}=\dfrac{3x^2+8x-3}{\left(x-3\right)\left(x+3\right)}\\ A=\dfrac{\left(3x-1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{3x-1}{x-3}\\ b,A< 2\Leftrightarrow\dfrac{3x-1-2x+6}{x-3}< 0\Leftrightarrow\dfrac{x+5}{x-3}< 0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+5>0\\x-3< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+5< 0\\x-3>0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-5\\x< 3\end{matrix}\right.\\\left\{{}\begin{matrix}x< -5\\x>3\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-5< x< 3\\x\in\varnothing\end{matrix}\right.\\ \Leftrightarrow-5< x< 3\)
\(c,A=\dfrac{3x-1}{x-3}=\dfrac{3\left(x-3\right)+8}{x-3}\in Z\Leftrightarrow3+\dfrac{8}{x-3}\in Z\\ \Leftrightarrow8⋮x-3\\ \Leftrightarrow x-3\inƯ\left(8\right)=\left\{-8;-4;-2;-1;1;2;4;8\right\}\\ \Leftrightarrow x\in\left\{-5;-1;1;2;4;5;7;11\right\}\left(tm\right)\)
