$$a \div ( b + c ) \neq ( a \div b ) + ( a \div c )$$
$\frac{a}{b+c}\neq \frac{a\left(b+c\right)}{bc}$
$\left\{\begin{matrix}\\c=-b\text{; }c=0\text{, }&\text{unconditionally}\\c\in \mathrm{R}\text{, }&b=0\text{ or }a\neq 0\end{matrix}\right.$
$\left\{\begin{matrix}\\b=0\text{; }b=-c\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&c=0\text{ or }a\neq 0\end{matrix}\right.$
