$\text{M = $\dfrac{1}{P}$ = $\dfrac{1}{\dfrac{x-1}{x^2}}$ = $\dfrac{x^2}{x-1}$ (x#0; x#1)}$
$\text{ Để M nguyên }$
=> $\dfrac{x^2}{x-1}$ nguyên
=> $\dfrac{x^2-1+1}{x-1}$ nguyên
=> $\dfrac{(x-1)(x+1)+1}{x-1}$ nguyên
=> $x+1+$$\dfrac{1}{x-1}$ nguyên
=> $\dfrac{1}{x-1}$ nguyên
$\text{=> x-1 là ước của 1}$
$\text{=> x-1 ∈ { 1; -1}}$
$\text{<=> x ∈ { 2; 0}}$
$\text{x=0 không thoả mãn ĐKXĐ}$
$\text{=> x = 2}$