\(a,P=\dfrac{x^2+x-x^2+x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{2}{x-1}\\ b,\left|x-1\right|=2\Leftrightarrow\left[{}\begin{matrix}x-1=2\\1-x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-1\left(ktm\right)\end{matrix}\right.\\ \Leftrightarrow P=\dfrac{2}{3-1}=1\\ c,P\in Z\Leftrightarrow x-1\inƯ\left(2\right)=\left\{-2;-1;1;2\right\}\\ \Leftrightarrow x\in\left\{0;2;3\right\}\left(x\ne-1\right)\)
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