[x/(x+y)+2y/(x+y)]*xy/(x+2y)÷(1/x+1/y)=[(x+2y)/(x+y)]*xy/(x+2y)÷(1/x+1/y)=(x+2y)/(x+y)*xy/(x+2y)÷(1/x+1/y)=xy/(x+y)÷[(y/(xy)+x/(xy)]=xy/(x+y)÷[(x+y)/(xy)]=xy/(x+y)*xy/(x+y)=1
