Problem

Source: Stars of Mathematics 2022, S3

Tags: algebra



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