Is this right?

Simplify by removing factors of 1.

2m^2+2m/10m^2+4m

My answer is

m^2/5m^2+2m

no,

removing a factor of 1 is ineffective, it changes nothing.

I will assume you mean
2m^2+2m/(10m^2+4m)

= 2m(m+1)/(2m(5m+2))
= (m+1)/(5m+2) , m ≠ 0, - 2, -2/5