fulcrum AAAAAAAAAAAAAAAA push rod BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB lever weight

The mechanical advantage of this lever is (A + B )/ A, not B/A. The reason is because for a lever that pivots at the fulcrum the torque at the push rod has to be equal to the torque at the lever weight. In other words the torque at the push rod is( A x push rod force) and the torque at the lever arm is (( A+B ) x lever weight).

then A x push rod force = ( A+B ) x lever weight

so then solving the equation ( A+B )/ A = push rod force/lever weight =Mechanical advantage