# Algebraic Simplification only multiplication in one step

I want to simplify an algebraic expression in Mathematica.

In[1] 1/a(2ba+ca+ba)
Out[1] 3b+c


but i want to multiply 1/a only. Not doing addition in same step. like

Out [2] (2b+c+b)


how can i calculate Out[2].

What you want to do cannot be done in a straightforward way. Mathematica will automatically evaluate your wanted result 2b+c+b to 3b+c. So we have to prevent the addition to be executed. That can be done by inactivating Plus:

Inactivate[1/a(2 b a + c a + b a), Plus]

(* (2 a b + a c + a b) / a *)


The multiplication is not distributed over Inactive[Plus]. So we have to do that ourselves:

%  /. x_ Inactive[Plus][y__] :> Inactive[Plus]  @@ (x {y})

(* 2 b + c + b *)


This looks like the result you want to have, but observe that the plus sign is grayed. It is Inactive[Plus] instead of Plus. Activating it again gives the normal Mathematica result:

Activate[%]

(* 3 b + c *)