Question 76
Let $a$, $b$ and $c$ be the sides of a triangle, that is: $a + b \gt c$, $b + c \gt a$ and $c + a \gt b$. Show that:
$$
\frac{a b + 1}{a^{2} + c a + 1} + \frac{b c + 1}{b^{2} + a b + 1} + \frac{c a + 1}{c^{2} + b c + 1} \gt \frac{3}{2}
$$
$$
\frac{a b + 1}{a^{2} + c a + 1} + \frac{b c + 1}{b^{2} + a b + 1} + \frac{c a + 1}{c^{2} + b c + 1} \gt \frac{3}{2}
$$