1/(a+1)-[(a+3)/a^2]*(a^2-2a+1)/(a^2+4a+3)=1/(a+1)-[(a+3)/a^2]*(a-1)^2/[(a+3)(a+1)]=1/(a+1)-(a-1)^2/[a^2*(a+1)]=[a^2-(a-1)^2]/[a^2*(a+1)]=(2a-1)/(a^3+a^2)[?]
