(a+2b)/(a+b)+2b^2/(a^2-b^2)
=[(a+2b)(a-b)+2b^2]/(a^2-b^2)
=(a^2+ab)/(a^2-b^2)
=a(a+b)/(a+b)(a-b)
=a/(a-b)
=(1/3)/(1/3-b)
=1/(1-3b)