x^3+y^3+7
=x^3+y^3+1-3xy+(6+3xy)
=(x+y+1)(x^2+y^2+1-xy-x-y)+(6+3xy)
なので
(x^3+y^3+7)/(x+y+1)
=x^2+y^2+1-xy-x-y+(6+3xy)/(x+y+1)