FindMaximum[{(
 p (4 t^2 V (-1 + [Alpha]) [Alpha] - 4 p^3 [Beta]2 +
 p^2 ([Beta]1^2 + [Beta]2 + 4 V [Beta]2 -
    4 t ([Alpha] - [Beta]2 + [Alpha] [Beta]2)) -
 p t (4 t [Alpha]^2 + [Beta]1^2 +
    4 V [Beta]2 - [Alpha] (1 + 4 t + [Beta]1^2 +
       4 V (1 + [Beta]2)))))/(
4 t (p + t (-1 + [Alpha])) (t [Alpha] + p [Beta]2))
 , 0 <= [Alpha] <= 1}, {[Alpha], 0}]