运用运算律计算:1/x+y+z*(1/x+1/y+1/z)×1/xy+yz+zx*1/xy+1/yz+1/zx
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运用运算律计算:1/x+y+z*(1/x+1/y+1/z)×1/xy+yz+zx*1/xy+1/yz+1/zx
![运用运算律计算:1/x+y+z*(1/x+1/y+1/z)×1/xy+yz+zx*1/xy+1/yz+1/zx](/uploads/image/z/1857575-47-5.jpg?t=%E8%BF%90%E7%94%A8%E8%BF%90%E7%AE%97%E5%BE%8B%E8%AE%A1%E7%AE%97%EF%BC%9A1%2Fx%2By%2Bz%2A%281%2Fx%2B1%2Fy%2B1%2Fz%29%C3%971%2Fxy%2Byz%2Bzx%2A1%2Fxy%2B1%2Fyz%2B1%2Fzx)
你的表达可能有点问题,是不是想求:
[1/(x+y+z)](1/x+1/y+1/z)[1/(xy+yz+zx)][1/(xy)+1/(yz)+1/(zx)]?
若是这样,则方法如下:
∵1/x+1/y+1/z=(yz+zx+xy)/(xyz),
∴(1/x+1/y+1/z)[1/(xy+yz+zx)]=1/(xyz).
∵1/(xy)+1/(yz)+1/(zx)=(z+x+y)/(xyz),
∴[1/(x+y+z)])][1/(xy)+1/(yz)+1/(zx)]=1/(xyz).
∴原式=1/(xyz)^2.
注:若原题不是我所猜测的那样,则请你补充说明.
[1/(x+y+z)](1/x+1/y+1/z)[1/(xy+yz+zx)][1/(xy)+1/(yz)+1/(zx)]?
若是这样,则方法如下:
∵1/x+1/y+1/z=(yz+zx+xy)/(xyz),
∴(1/x+1/y+1/z)[1/(xy+yz+zx)]=1/(xyz).
∵1/(xy)+1/(yz)+1/(zx)=(z+x+y)/(xyz),
∴[1/(x+y+z)])][1/(xy)+1/(yz)+1/(zx)]=1/(xyz).
∴原式=1/(xyz)^2.
注:若原题不是我所猜测的那样,则请你补充说明.
运用运算律计算:1/x+y+z*(1/x+1/y+1/z)×1/xy+yz+zx*1/xy+1/yz+1/zx
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