Let f, g:(1, ∞) → R be defined as f(x)=(2 x+3)/(5 x+2) and g(x)=(2-3 x)/(1-x). If the range of the function f ° g:[2,4] → R is [α, β], then 1/(β-α)…

Let $\displaystyle f, g:(1, \infty) \rightarrow \mathbb{R}$ be defined as $\displaystyle f(x)=\frac{2 x+3}{5 x+2}$ and $\displaystyle g(x)=\frac{2-3 x}{1-x}$. If the range of the function $\displaystyle f \circ g:[2,4] \rightarrow \mathbb{R}$ is $\displaystyle [\alpha, \beta]$, then $\displaystyle \frac{1}{\beta-\alpha}$ is equal to