(a/a+1)+(b/b+1)+(c/c+1)
=[1/1+(1/a)] +[1/1+(1/b)]+[1/1+(1/c)]
代入得
1/(x+y+z/x)+1/(x+y+z/y)+1/(x+y+z/z)
=(x+y+z)/(x+y+z)=1