VTMO 2026 - Grade 8 - Final - SET 5 - Self-study Question 3

Let $a,b,c$ be pairwise distinct. Simplify $$A=\left(\frac1{(a-b)^2}+\frac1{(b-c)^2}+\frac1{(c-a)^2}\right):\left(\frac1{a-b}+\frac1{b-c}+\frac1{c-a}\right)^2.$$