mo=.
fx = .
fy=.
m1 = mo - fy x
m2 = mo - fy la - fx x

theta = Expand[Integrate[m1/sa D[m1,mo],{x,0,la}] + Integrate[m2/sb D[m2,mo],{x,0,lb}]]

rule1 = Solve[theta==0, mo]

Expand[mo /. rule1[[1]][[1]]]

mo = %

dy = Expand[Integrate[m1/sa D[m1,fy],{x,0,la}] + Integrate[m2/sb D[m2,fy],{x,0,lb}]]

rule2 = Solve[dy==0, fy];
Expand[fy /. rule2[[1]][[1]]];
fy=%

dx = Expand[Integrate[m1/sa D[m1,fx],{x,0,la}] + Integrate[m2/sb D[m2,fx],{x,0,lb}]]

Simplify[%]

mo

Simplify[%]