value of the expression (x^2 - x + 1)/(x - 1) cannot lie between
a) 1,-3
b) -1,-3
c) -4,2
d) -4,-2

Let (x^2 - x + 1)/(x-1) = k
Therefore, x^2 - x + 1 = kx - k
Or, x^2 - (k+1)*x + (k+1) = 0

For this equation to have real roots, the discriminant should be greater than zero.
So, (k+1)^2 >= 4*(k+1)
Or, (k+1)(k-3) >= 0

Therefore, k can't lie between (-1,3)

Take a look at this formula sheet for CAT, it might be useful for you.

Why k+1