Question 21
Prove: if for non-zero real numbers $a, b$ and $c$ we have
$$
a(b+c)+b(c+a)+c(a+b)=a b+b c+c a
$$
then the value of the expression $\frac{a^{2}(b+c)+b^{2}(a+c)+c^{2}(a+b)}{a b c}$ is an integer.
$$
a(b+c)+b(c+a)+c(a+b)=a b+b c+c a
$$
then the value of the expression $\frac{a^{2}(b+c)+b^{2}(a+c)+c^{2}(a+b)}{a b c}$ is an integer.