a, \(A\in Z\Rightarrow2x+3⋮x-3\)
\(\Rightarrow2x-6+9⋮x-3\)
\(\Rightarrow2\left(x-3\right)+9⋮x-3\)
\(\Rightarrow9⋮x-3\)
\(\Rightarrow x-3\in\left\{1;-1;3;-3;9;-9\right\}\)
\(\Rightarrow x\in\left\{4;2;6;0;12;-6\right\}\)
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b, \(B\in Z\Rightarrow2x^2+x-5⋮2x+1\)
\(\Rightarrow x\left(2x+1\right)-5⋮2x+1\)
\(\Rightarrow5⋮2x+1\)
\(\Rightarrow2x+1\in\left\{1;-1;5;-5\right\}\)
\(\Rightarrow x\in\left\{0;-1;2;-3\right\}\)
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