1: \(P=\dfrac{2x-5}{x\left(x-1\right)}-\dfrac{x+5}{x}+\dfrac{2x+5}{x-1}\)
\(=\dfrac{2x-5-\left(x+5\right)\left(x-1\right)+x\left(2x+5\right)}{x\left(x-1\right)}\)
\(=\dfrac{2x-5-\left(x^2+4x-5\right)+2x^2+5x}{x\left(x-1\right)}\)
\(=\dfrac{2x^2+7x-5-x^2-4x+5}{x\left(x-1\right)}\)
\(=\dfrac{x^2+3x}{x\left(x-1\right)}=\dfrac{x\left(x+3\right)}{x\left(x-1\right)}=\dfrac{x+3}{x-1}\)
2: \(x^2-1=0\)
=>\(x^2=1\)
=>\(\left[{}\begin{matrix}x=1\left(loại\right)\\x=-1\left(nhận\right)\end{matrix}\right.\)
Thay x=-1 vào P, ta được:
\(P=\dfrac{-1+3}{-1-1}=\dfrac{2}{-2}=-1\)
3: P<1
=>P-1<0
=>\(\dfrac{x+3}{x-1}-1< 0\)
=>\(\dfrac{x+3-x+1}{x-1}< 0\)
=>\(\dfrac{4}{x-1}< 0\)
=>x-1<0
=>x<1
Kết hợp ĐKXĐ, ta được: \(\left\{{}\begin{matrix}x< 1\\x\ne0\end{matrix}\right.\)