\(a,A=\dfrac{2^2-9}{3\left(2+5\right)}=\dfrac{-5}{21}\\ b,B=\dfrac{x^2-3x+2x^2+6x-3x^2-9}{\left(x-3\right)\left(x+3\right)}=\dfrac{3x-9}{\left(x-3\right)\left(x+3\right)}\\ B=\dfrac{3\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{3}{x+3}\\ c,P=AB=\dfrac{\left(x-3\right)\left(x+3\right)}{3\left(x+5\right)}\cdot\dfrac{3}{x+3}=\dfrac{x-3}{x+5}\\ P=\dfrac{x+5-8}{x+5}=1-\dfrac{8}{x+5}\in Z\\ \Leftrightarrow x+5\inƯ\left(8\right)=\left\{-8;-4;-2;-1;1;2;4;8\right\}\\ \Leftrightarrow x\in\left\{-13;-9;-7;-6;-4;-1\right\}\left(x\ne\pm3\right)\)
\(a.\) \(Thay\) \(x=2\left(TM\right):\) \(\dfrac{2^2-9}{3\left(2+5\right)}=\dfrac{-5}{21}.\)
\(b.\) \(B=\dfrac{x}{x+3}+\dfrac{2x}{x-3}-\dfrac{3x^2+9}{x^2-9}.\) \(\left(x\ne-5;x\ne3;x\ne-3\right).\)
\(B=\dfrac{x\left(x-3\right)+2x\left(x+3\right)-3x^2-9}{\left(x-3\right)\left(x+3\right)}.\)
\(B=\dfrac{x^2-3x+2x^2+6x-3x^2-9}{\left(x-3\right)\left(x+3\right)}=\dfrac{3x-9}{\left(x-3\right)\left(x+3\right)}.\)
\(B=\dfrac{3\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{3}{x+3}.\)
\(c.\) \(P=A.B.\Rightarrow P=\dfrac{x^2-9}{3\left(x+5\right)}.\dfrac{3}{x+3}=\dfrac{x-3}{x+5}=1+\dfrac{-8}{x+5}.\)
Để \(P\in Z.\Leftrightarrow1+\dfrac{-8}{x+5}\in Z.\Leftrightarrow x+5\in\) Ư \(\left(-8\right)=\left(1;-1;2;-2;4;-4;8;-8\right).\)
\(\Rightarrow x\in\left\{-4;-6;-7;-1;-9;-13\right\}.\)
