(9/(a^2+3a+9)+2a/(a-3)-(a^3+15^2)/(a^3-27))*(a-3+9a/(a-3))*(1/(a-3))=(9*(a-3)+2a(a^2+3a+9)-a^3-15a^2)/(a^3-27))*(((a-3)^2+9a)/(a-3))*(1/(a-3))=((9a-27+2a^3+6a^2+18a-a^3-15a^2)/(a^3-27))*((a^2-6a+9+9a)/(a-3))*(1/(a-3))=((a^3-9a^2+27a-27)/((a-3)(a^2+3a+9))*((a^2+3a+9)/(a-3)^2)=(a^3-9a^2+27a-27)/(a-3)^3=((a^3-27)-(9a^2-27a))/(a-3)^3=((a-3)(a^2+3a+9)-9a(a-3))/(a-3)^3=((a-3)(a^2+3a+9-9a))/(a-3)^3=(a^2-6a+9)/(a-3)^2=(a-3)^2/(a-3)^2=1