`2/[a-1]=a` `ĐK: a \ne 1`
`=>2=a(a-1)`
`<=>a^2-a-2=0`
`<=>a^2+a-2a-2=0`
`<=>(a-2)(a+1)=0`
`<=>[(a=2),(a=-1):}` (t/m)
\(\dfrac{2}{a-1}=a\)
\(\Rightarrow\dfrac{2}{a-1}=\dfrac{a\left(a-1\right)}{a-1}\)
\(\Rightarrow2=a^2-a\)
\(\Leftrightarrow-a^2+a+2=0\)
\(\Rightarrow-a^2-2a+a+2=0\)
\(\Rightarrow-a\left(a+2\right)+\left(a+2\right)=0\)
\(\Rightarrow\left(-a+1\right)\left(a+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}-a+1=0\\a+2=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}a=1\\a=-2\end{matrix}\right.\)
Vậy khi \(a\in\left\{1;-2\right\}\) thì \(P=\dfrac{2}{a-1}=a\)
