\(A=\dfrac{4+\sqrt{15}}{4-\sqrt{15}}+\dfrac{4-\sqrt{15}}{4+\sqrt{15}}\)
\(=\dfrac{\left(4+\sqrt{15}\right)^2+\left(4-\sqrt{15}\right)^2}{\left(4-\sqrt{15}\right)\left(4+\sqrt{15}\right)}\)
\(=\dfrac{\left(16+8\sqrt{15}+15\right)+\left(16-8\sqrt{15}+15\right)}{16-15}\)
\(=\dfrac{62}{1}=62\)