Let \(f, \mathrm{~g}:(1, \infty) \rightarrow \mathbb{R}\) be defined as \(f(\mathrm{x})=\frac{2 x+3}{5 x+2}\) and \(\mat…

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

[JEE Main 2025, 4 Apr (Shift 1)]