LH

cho x.y.z=2010. CMR 

\(\frac{2010x}{xy+2010x+2010}+\frac{y}{yz+y+2010}+\frac{z}{xz+z+1}=1\)

TA
4 tháng 4 2018 lúc 14:18

\(\frac{2010x}{xy+2010x+2010}+\frac{y}{yz+y+2010}+\frac{z}{xz+z+1}\)

\(=\frac{x^2yz}{xy+x^2yz+xyz}+\frac{y}{yz+y+xyz}+\frac{z}{xz+z+1}\)

\(=\frac{xz}{xz+z+1}+\frac{1}{xz+z+1}+\frac{z}{xz+z+1}\)

\(=\frac{xz+z+1}{xz+z+1}=1\)

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