rce=2y''[t]+3y'[t]+7y[t]==5u[t]-u'[t]

myLapl[co_]:=LaplaceTransform[co,t,p];
myLapl[rce]/.{LaplaceTransform[y[t],t,p]->Y[p],LaplaceTransform[u[t],t,p]->U[p]};
Solve[%,Y[p]][[1,1]]/.(a_->b_):>a==b;
uprce=%/.{u[0]->0,y[0]->0,y'[0]->0}

Denominator[uprce[[2]]]==0
N@Solve[%]

Expand[(p+6)*(p+2)]

prenos=Simplify[(1/(12+8 p+(p^2)))]

Apart[prenos]