(1/a+1/b)*((a+b)^2-(a^3-b^3)/a-b

(1/a+1/b)*((a+b)^2-(a^3-b^3)/a-b=(1/а+1/в)((а^2+2ав+в^2)-(а-в)(а^2+ав+в^2)/а-в)=(1/а+1/в)(а^2+2ав+в^2-а^2-ав-в^2)= (1/а+1/в)ав=в+а.