若x+y+z不等于0,a=x/y+z,b=y/x+z,c=z/x+y,则a/(a+1)+b/(b+1)+c/c+1=
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若x+y+z不等于0,a=x/y+z,b=y/x+z,c=z/x+y,则a/(a+1)+b/(b+1)+c/c+1=
若x+y+z不等于0,a=x/y+z,b=y/x+z,c=z/x+y,则a/(a+1)+b/(b+1)+c/c+1=
若x+y+z不等于0,a=x/y+z,b=y/x+z,c=z/x+y,则a/(a+1)+b/(b+1)+c/c+1=
a+1=1+x/(y+z)
=(y+z)/(y+z)+x/(y+z)
=(x+y+z)/(y+z)
a/(a+1)=[x/(y+z)]/[(x+y+z)/(y+z)]
=x/(x+y+z)
同理:b/(b+1)=y/(x+y+z)
c/(c+1)=z/(x+y+z)
所以:a/(a+1)+b/(b+1)+c/(c+1)
=x/(x+y+z)+y/(x+y+z)+z/(x+y+z)
=(x+y+z)/(x+y+z)
=1
所以:a/(a+1)+b/(b+1)+c/(c+1)=1
∵a=x/(y+z)
∴a+1=x+y+z/(y+z)
∴a/(a+1)=x/(x+y+z)
同理:b/(b+1)=y/(x+y+z), c/(c+1)=z/(x+y+z)
∴a/(a+1)+b/(b+1)+c/(c+1)=x/(x+y+z)+y/(x+y+z)+z/(x+y+z)=(x+y+z)/(x+y+z)=1
即:a/(a+1)+b/(b+1)+c/(c+1)=1
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