Simplify[D[(((3/10) t)/((t+2) (t+a))),t]]

Expand[(t+2) (t+a)]

Solve[-((3 (-2 a+(t^2)))/(10 (((2+t))^2) (((a+t))^2)))==0,t]

a+(b/(1+Exp[-(((x-d))/c)]))

Plot[(((3/10) t)/((t+2) (t+a))),{t,0,10},PlotRange->{0,.03}]

Manipulate[Plot[(((3/10) t)/((t+2) (t+a))),{t,0,10},PlotRange->{0,.03}],{a,5,10}]