[x/(x+y)+2y/(x+y)]×[xy/(x+2y)]÷(1/x+1/y)=[(x+2y)/(x+y)]×[xy/(x+2y)]÷[(x+y)/xy]=[xy/(x+y)]×[xy/(x+y)]=x²y²/(x+y)²
(X/X+Y + 2Y/X+Y)×xy/x+2y÷(1/X+1/Y)=(x+2y)/(x+y)×xy/(x+2y)×(x+y)/xy=1