Let f(x)=5-|x-2| and g(x)=|x+1|, x ∈ R. If f(x) attains maximum value at α and g(x) attains minimum value at β, then lim_x →-α β ((x-1)(x^2-5…

Let $\displaystyle f(x)=5-|x-2|$ and $\displaystyle g(x)=|x+1|$, $\displaystyle x \in \mathbf{R}$. If $\displaystyle f(x)$ attains maximum value at $\displaystyle \alpha$ and $\displaystyle g(x)$ attains minimum value at $\displaystyle \beta$, then $\displaystyle \lim _{x \rightarrow-\alpha \beta} \frac{(x-1)\left(x^2-5 x+6\right)}{x^2-6 x+8}$ is equal to :