$$\left. \begin{array} { l } { a + b + c = 0 \frac { b - c } { a } + \frac { c - a } { b } + \frac { a - b } { c } = 0 } \\ { b c + b = c } \\ { b ^ { 2 } c ^ { 2 } + \frac { c a + c \right.$$
$a\neq 0\text{, }b=-2\text{, }c=2$
$a=\frac{b-1}{2b+1}\text{, }b\in \mathrm{R}\setminus 1,-\frac{1}{2},0\text{, }c=-1$
$a=-\left(2b-1\right)\left(b+1\right)\text{, }b\in \mathrm{R}\setminus 0,-1,\frac{1}{2}\text{, }c=1$
$a=-\frac{\left(b+c\right)\left(bc+b-c\right)}{bc-b+c}\text{, }b\in \mathrm{R}\setminus -\frac{c}{c-1},0,-c,\frac{c}{c+1}\text{, }c\in \mathrm{R}\setminus 0,1,-1$
