How to make result arrangement for the variable?

I was calculating equations,

p2 := 1 e + r M1^2
p1 := 1 + r M2^2
p2/p1/.M2-> Sqrt[((r - 1)/(2 r))]
Simplify@%/.e -> 0


where e : to remove by approximation that M1 is close to infinite(term of M1 is very large then other term, since neglect other term)

This results is

(2 M1^2 r)/(1 + r)


I want to make result as

(2 r)/(1 + r) *  M1^2


And why these result cannot be simple form

T2 := 1 ϵ + (r - 1)/2 M1^2
T1 := 1 + (r - 1)/2 M2^2
ρ2 := M1 Sqrt[T1]
ρ1 := M2 Sqrt[T2]
$Assumtions = r > 0;$Assumtions = M1 > 1;
ρ2/ρ1 // Refine // FullSimplify
% /. M2 -> Sqrt[(r - 1)/(2 r)]
% /. ϵ -> 0 // Simplify


p2 := 1 e + r M1^2
p1 := 1 + r M2^2
p2/p1 /. M2 -> Sqrt[((r - 1)/(2 r))]
expr = Simplify@% /. e -> 0


If you want a non-standard (to Mathematica) form you have to force it

Inactive[Times][Coefficient[expr, M1^2], M1^2]


You misspelled $Assumptions T2 := 1 ϵ + (r - 1)/2 M1^2 T1 := 1 + (r - 1)/2 M2^2 ρ2 := M1 Sqrt[T1] ρ1 := M2 Sqrt[T2]$Assumptions = {r > 0, M1 > 1};
ρ2/ρ1 // FullSimplify (* Refine is unnecessary *)
% /. M2 -> Sqrt[(r - 1)/(2 r)]
% /. ϵ -> 0 // Simplify