\(-1< x< 1\Rightarrow5-3x>0\Rightarrow A>0\)
\(A^2=\dfrac{\left(5-3x\right)^2}{1-x^2}=\dfrac{9x^2-30x+25}{1-x^2}=\dfrac{16-16x^2+9-30x+25x^2}{1-x^2}=16+\dfrac{\left(3-5x\right)^2}{1-x^2}\ge16\)
\(\Rightarrow A\ge4\)
\(A_{min}=4\) khi \(x=\dfrac{3}{5}\)