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已知1/x+1/(y+z)=1/2,1/y+1/(z+x)=1/3,1/z+1/（x+y）=1/4,则2/x+3/Y+4/z的值为
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已知1/x+1/(y+z)=1/2,1/y+1/(z+x)=1/3,1/z+1/（x+y）=1/4,则2/x+3/Y+4/z的值为
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答案和解析
1/x+1/(y+z)=1/2,
(x+y+z)/[x(y+z)]=1/2
即 1/x =(y+z)/[2(x+y+z)]
同样可得：
1/y=(x+z)/[3(x+y+z)]
1/z=(x+y)/[4(x+y+z)]
所以：
2/x+3/y+4/z
=(y+z)/(x+y+z)+(x+z)/(x+y+z)+(x+y)/(x+y+z)
=2(x+y+z)/(x+y+z)
=2
(x+y+z)/[x(y+z)]=1/2
即 1/x =(y+z)/[2(x+y+z)]
同样可得：
1/y=(x+z)/[3(x+y+z)]
1/z=(x+y)/[4(x+y+z)]
所以：
2/x+3/y+4/z
=(y+z)/(x+y+z)+(x+z)/(x+y+z)+(x+y)/(x+y+z)
=2(x+y+z)/(x+y+z)
=2
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