\(a,B=\dfrac{-2}{2\cdot4+1}=-\dfrac{2}{9}\\ b,A=\dfrac{x^2-3x+2x+6-x^2-3}{\left(x-3\right)\left(x+3\right)}=\dfrac{-x+3}{\left(x-3\right)\left(x+3\right)}=\dfrac{-1}{x+3}\\ c,P=2A:B=\dfrac{-2}{x+3}\cdot\dfrac{2x+1}{-2}=\dfrac{2x+1}{x+3}=2-\dfrac{5}{x+3}\in Z\\ \Leftrightarrow x+3\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\\ \Leftrightarrow x\in\left\{-8;-4;-2;2\right\}\left(tm\right)\)