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