If the domain of the function \(f\left(x\right)={\log }_{\mathrm{e}}\left(\frac{2\mathrm{x}-3}{5+4\mathrm{x}}\right)+{\s…

If the domain of the function \(f\left(x\right)={\log }_{\mathrm{e}}\left(\frac{2\mathrm{x}-3}{5+4\mathrm{x}}\right)+{\sin }^{-1}\left(\frac{4+3\mathrm{x}}{2-\mathrm{x}}\right)\) is \([\alpha ,\beta )\), then \({\alpha }^{2}+4\beta\) is equal to

[JEE Main 2025, 3 Apr (Shift 1)]