"Spoooooooky" Russian rational expressions 17

$\Rightarrow \left( \dfrac{a-1}{3a + (a-1)^2} - \dfrac{1 - 3a + a^2}{a^3 - 1} - \dfrac{1}{a-1} \right) \div \dfrac{a^2 + 1}{1-a}$

$\implies \left(\dfrac{a-1}{3a+a^2+1-2a}-\dfrac{1-3a+a^2}{(a-1)(a^2+1+a)}-\dfrac{1}{a-1}\right)×\dfrac{1-a}{a^2+1}$

$\implies \left(\dfrac{(a-1)^2}{(a-1)(a^2+1+a)}-\dfrac{1-3a+a^2}{(a-1)(a^2+1+a)}-\dfrac{a^2+1+a}{(a-1)(a^2+1+a)}\right)×\dfrac{1-a}{a^2+1}$

$\implies \left(\dfrac{a^2+1-2a-1+3a-a^2-a^2-1-a}{(a-1)(a^2+1+a)}\right)×\dfrac{1-a}{a^2+1}$

$\implies \dfrac{-(a^2+1)}{(a-1)(a^2+1+a)}×\dfrac{1-a}{a^2+1}$

$\implies \dfrac{1}{a^2+1+a}$

Pluging $a=2016$ .

$\dfrac{1}{(2016×2017)+1}=\dfrac{1}{4066273}$

$\therefore x+y=\boxed{4066274}$