(m/m-2)-(m^2-2m+4)/(m-2)(m+2) *(m+2)/(2-m)
=(m/m-2)+(m^2-2m+4)/(m-2)^2
=(m(m-2)+(m^2-2m+4))/(m-2)^2
=2(m-2)(m-1)/(m-2)^2
=2(m-1)/(m-2)