Question 114
Let $a$, $b$, $c$, $d$ be real numbers such that $ab(c+d) = cd(a+b)$. Prove that
$$
\frac{a+1}{a^2+3} + \frac{b+1}{b^2+3} \ge \frac{c-1}{c^2+3} + \frac{d-1}{d^2+3}.
$$
$$
\frac{a+1}{a^2+3} + \frac{b+1}{b^2+3} \ge \frac{c-1}{c^2+3} + \frac{d-1}{d^2+3}.
$$