(m-n)/(m+2n)+(m^2-n^2)/(m^2+4mn+4n^2)
= (m-n)/(m+2n)+(m-n)(m+n)/(m+2n)^2
=[(m-n)(m+2n)+(m-n)(m+n)]/(m+2n)^2
=(m-n)(m+2n+m+n)/(m+2n)^2
=(m-n)(2m+3n)/(m+2n)^2
(m-n)/(m+2n)+(m^2-n^2)/(m^2+4mn+4n^2)
= (m-n)/(m+2n)+(m-n)(m+n)/(m+2n)^2
=[(m-n)(m+2n)+(m-n)(m+n)]/(m+2n)^2
=(m-n)(m+2n+m+n)/(m+2n)^2
=(m-n)(2m+3n)/(m+2n)^2