if a,b,c are roots of a cubic equation then for the following question... If $a, b, c$ are roots of $x^3 -3x^2 + 2x +4 = 0$ and
$$y= 1 + \frac{a}{x-a} + \frac{bx}{(x-a)(x-b)} + \frac{cx^2}{(x-a)(x-b)(x-c)}$$
then value of $y$ at $x=2$ is:

$$1+\dfrac a{x-a}=\dfrac x{x-a}$$
$$1+\dfrac a{x-a}+\dfrac{bx}{(x-a)(x-b)} =x\left[\dfrac1{x-a}+\dfrac b{(x-a)(x-b)}\right]=\dfrac{x^2}{(x-a)(x-b)}$$
$$1 + \frac{a}{x-a} + \frac{bx}{(x-a)(x-b)} + \frac{cx^2}{(x-a)(x-b)(x-c)}=\cdots=\dfrac{x^3}{(x-a)(x-b)(x-c)}$$
