a) Điều kiện : \(\left\{{}\begin{matrix}x\ne0\\x\ne1\\x\ne-1\end{matrix}\right.\)
P =\(\dfrac{x.\left(x+1\right)}{\left(x-1\right)^2}:\left(\dfrac{\left(x+1\right).\left(x-1\right)}{x.\left(x-1\right)}+\dfrac{x}{x.\left(x-1\right)}+\dfrac{2-x^2}{x.\left(x-1\right)}\right)\)
P =\(\dfrac{x.\left(x+1\right)}{\left(x-1\right)^2}:\dfrac{x^2-1+x+2-x^2}{x.\left(x-1\right)}\)
P =\(\dfrac{x.\left(x+1\right)}{\left(x-1\right)^2}:\dfrac{x+1}{x.\left(x-1\right)}=\dfrac{x.\left(x+1\right)}{\left(x-1\right)^2}.\dfrac{x.\left(x-1\right)}{x+1}=\dfrac{x^2}{x-1}\)
b) P = \(\dfrac{-1}{2}\Leftrightarrow\) P = \(\dfrac{x^2}{x-1}=\dfrac{-1}{2}\) với x thỏa mãn điều kiện
\(\Rightarrow2x^2=-x+1\Leftrightarrow2x^2+x-1=0\Leftrightarrow2x^2+2x-x-1=0\)
\(\Leftrightarrow\left(2x-1\right).\left(x+1\right)=0\Leftrightarrow x=\dfrac{1}{2}\) (thỏa mãn)
Hoặc x = -1 (không thỏa mãn)
Vậy P =\(\dfrac{-1}{2}\Leftrightarrow x=\dfrac{1}{2}\)
