(a/a+2-1/a^2+2a)/a/a+2
=(1+2-1/a^2+2a)/a/a+2
=(3-1/a^2+2a)/a/a+2
=(3a^2/a^2-1/a^2+2a^3/a^2)/a²+2
=[(3a^2-1+2a^3)/a^2)/a²+2
=[(2a^3+3a^2-1)/a^2)/a²+2
=(2a^3+3a^2-1)/a^4+2
=(2a^3+3a^2-1)/a^4+2a^4/a^4
=(2a^4+2a^3+3a^2-1)/a^4