It is given that $y=\frac{{{x}^{2}}+x+1}{x-1}$, $x\in \mathbb{R}$, $x
e 1$. Without using a calcula

Question

It is given that $y=\frac{{{x}^{2}}+x+1}{x-1}$, $x\in \mathbb{R}$, $x
e 1$. Without using a calculator, find the set of values that $y$ can take. [5]

Accepted Answer

$y \leq 3-2\sqrt 3 or y \geq 3+2\sqrt 3$

N2013 P1 Q2