Question

\(CMR:\frac{a}{ab+a+1}+\frac{b}{bc+b+1}+\frac{c}{ac+c+1}=1\)       biết

\(abc=1\)

Answer 1

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Answer 2

Thay abc = 1 vào biểu thức:

\(\frac{a}{ab+a+1}+\frac{b}{bc+b+1}+\frac{c}{ac+c+1}=\frac{a}{a.\left(b+1+bc\right)}+\frac{b}{bc+b+1}+\frac{c}{c.a.\left(b+1+bc\right)}.\)

\(=\frac{a}{a.\left(b+1+bc\right)}+\frac{ba}{a.\left(bc+b+1\right)}+\frac{1}{a.\left(b+1+bc\right)}\)

\(=\frac{ab+a+1}{a.\left(b+1+bc\right)}=\frac{a.\left(b+1+bc\right)}{a.\left(b+1+bc\right)}=1\)

=> đpcm