ĐKXĐ: \(x\ne\left\{3;4\right\}\)
\(Q=\frac{12x-45}{\left(x-3\right)\left(x-4\right)}-\frac{\left(x-3\right)\left(x+5\right)}{\left(x-3\right)\left(x-4\right)}-\frac{\left(2x+3\right)\left(x-4\right)}{\left(x-3\right)\left(x-4\right)}\)
\(=\frac{12x-45-x^2-2x+15-2x^2+5x+12}{\left(x-3\right)\left(x-4\right)}=\frac{-3x^2+15x-18}{\left(x-3\right)\left(x-4\right)}\)
\(=\frac{-3\left(x-2\right)\left(x-3\right)}{\left(x-3\right)\left(x-4\right)}=\frac{-3\left(x-2\right)}{x-4}\)
\(\left|x\right|=3\Rightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}Q=3\\Q=-\frac{15}{7}\end{matrix}\right.\)
\(Q=\frac{-3\left(x-4\right)-6}{x-4}=-3-\frac{6}{x-4}\)
Để Q nguyên \(\Rightarrow x-4=Ư\left(6\right)=\left\{-6;-3;-2;-1;1;2;3;6\right\}\)
\(\Rightarrow x=\left\{-2;1;2;5;6;7;10\right\}\)
