1/y+1/x∝1/(x+y) ⟹1/y+1/x=k/(x+y); where, k is constant of variation. ⟹(x+y)/xy=k/(x+y) ⟹(x+y)^2=kxy ⟹x^2+2xy+y^2=kxy ⟹x^2−(k-2)xy+y^2=0 ⟹x^2−mxy+y^2=0; where, m=k-2=constant. ⟹(x/y)^2−m(x/y)+1=0 [On dividing both the sides by y^2.] ⟹x/y=[m±√(m^2−4)]/2=a constant=l(say) [By quadratic formula.] ⟹x=ly ∴x∝y.