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

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

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