A = (((vdown ( 1 - m ) d + vup ( 1 - d ) ( 1 + m )) )/(1 - m ( 1 - 2 d )));
B = (((vdown ( 1 + m ) d + vup ( 1 - d ) ( 1 - m )) )/(1 + m ( 1 - 2 d )));
spread=Simplify[A-B]

spread/.{d->(1/2)}