[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
[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