a. \(x\ne1,x\ne3\)
\(P=\left(1+\dfrac{1}{x-1}\right)\left(\dfrac{x^2-7}{x^2-4x+3}+\dfrac{1}{x-1}+\dfrac{1}{3-x}\right)\)
\(P=\left(\dfrac{x}{x-1}\right)\left(\dfrac{x^2-7}{\left(x-1\right)\left(x-3\right)}+\dfrac{1}{x-1}-\dfrac{1}{x-3}\right)\)
\(P=\dfrac{x}{x-1}\left(\dfrac{x^2-7+x-3-x+1}{\left(x-1\right)\left(x-3\right)}\right)=\dfrac{x}{x-1}.\dfrac{x^2-9}{\left(x-1\right)\left(x-3\right)}\)
\(P=\dfrac{x}{x-1}.\dfrac{\left(x-3\right)\left(x+3\right)}{\left(x-1\right)\left(x-3\right)}=\dfrac{x^2+3x}{\left(x-1\right)^2}\)
b. \(\left|x+2\right|=5\Leftrightarrow\left[{}\begin{matrix}x=3\left(loại\right)\\x=-7\end{matrix}\right.\)
\(P=\dfrac{49-21}{64}=\dfrac{7}{16}\)
c. \(P>1\Leftrightarrow\dfrac{x^2+3x}{\left(x-1\right)^2}>1\left(x\ne1\right)\)
\(\Leftrightarrow\dfrac{x^2+3x-x^2+2x-1}{\left(x-1\right)^2}>0\Leftrightarrow\dfrac{5x-1}{\left(x-1\right)^2}>0\)
\(\Leftrightarrow5x-1>0\Leftrightarrow x>\dfrac{1}{5}\)
