\(a+b-\left(\frac{1}{a}+\frac{1}{b}\right)+c-\frac{1}{c}=0\)\(\Leftrightarrow\left(a+b\right)\left(1-\frac{1}{ab}\right)-\frac{\left(1-c\right)\left(1+c\right)}{c}=0\)
\(\Leftrightarrow\left(a+b\right)\left(1-c\right)-\frac{\left(1-c\right)\left(1+c\right)}{c}=0\)
\(\Leftrightarrow\left(1-c\right)\left(a+b-\frac{1+c}{c}\right)=0\Leftrightarrow\left(1-c\right)\left(a+b-\frac{abc+c}{c}\right)=0\)
\(\Leftrightarrow\left(1-c\right)\left(a+b-ab-1\right)=0\) \(\Leftrightarrow\left(1-c\right)\left(a\left(1-b\right)-\left(1-b\right)\right)=0\)
\(\Leftrightarrow\left(1-c\right)\left(1-b\right)\left(a-1\right)=0\Leftrightarrow\left[{}\begin{matrix}a=1\\b=1\\c=1\end{matrix}\right.\)
Vậy trong 3 số có ít nhất 1 số bằng 1
