Để A là số nguyên thì \(-2x-6+7⋮x+3\)
\(\Leftrightarrow x+3\in\left\{1;-1;7;-7\right\}\)
hay \(x\in\left\{-2;-4;4;-10\right\}\)
Khi x=-2 thì \(A=\dfrac{-2\cdot\left(-2\right)+1}{-2+3}=4+1=5\)
Khi x=-4 thì \(A=\dfrac{1+2\cdot4}{-4+3}=-9\)
Khi x=4 thì \(A=\dfrac{1-2\cdot4}{4+3}=-1\)
Khi x=-10 thì \(A=\dfrac{1+2\cdot10}{-10+3}=-3\)