数学高手解一道分式计算题,一定要写过程x.y.z为实数,且xy/x+y=1/3,yz/y+z=1/4,xz/x+z=1/5,求xyz/xy+yz+zx
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![数学高手解一道分式计算题,一定要写过程x.y.z为实数,且xy/x+y=1/3,yz/y+z=1/4,xz/x+z=1/5,求xyz/xy+yz+zx](/uploads/image/z/225719-71-9.jpg?t=%E6%95%B0%E5%AD%A6%E9%AB%98%E6%89%8B%E8%A7%A3%E4%B8%80%E9%81%93%E5%88%86%E5%BC%8F%E8%AE%A1%E7%AE%97%E9%A2%98%2C%E4%B8%80%E5%AE%9A%E8%A6%81%E5%86%99%E8%BF%87%E7%A8%8Bx.y.z%E4%B8%BA%E5%AE%9E%E6%95%B0%2C%E4%B8%94xy%2Fx%2By%3D1%2F3%2Cyz%2Fy%2Bz%3D1%2F4%2Cxz%2Fx%2Bz%3D1%2F5%2C%E6%B1%82xyz%2Fxy%2Byz%2Bzx)
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数学高手解一道分式计算题,一定要写过程x.y.z为实数,且xy/x+y=1/3,yz/y+z=1/4,xz/x+z=1/5,求xyz/xy+yz+zx
数学高手解一道分式计算题,一定要写过程
x.y.z为实数,且xy/x+y=1/3,yz/y+z=1/4,xz/x+z=1/5,求xyz/xy+yz+zx
数学高手解一道分式计算题,一定要写过程x.y.z为实数,且xy/x+y=1/3,yz/y+z=1/4,xz/x+z=1/5,求xyz/xy+yz+zx
分别取倒数:
xy/(x+y)=1/3=>1/x+1/y=3……1
yz/(y+z)=1/4=>1/y+1/z=4……2
xz/(x+z)=1/5=>1/x+1/z=5……3
1式+2式+3式得:
2(1/x+1/y+1/z)=12
1/x+1/y+1/z=6
再取倒数得:
xyz/xy+yz+zx =1/6!
完!
6
xy/(x+y)=1/3=>1/x+1/y=3……1
yz/(y+z)=1/4=>1/y+1/z=4……2
xz/(x+z)=1/5=>1/x+1/z=5……3