MathNet 2023-part-07 — 187 problems (EN–VI) Question 28

Nonzero real numbers $a, b, c$ satisfy the equation $ab + bc + ac = 0$. Prove that the numbers $a + b + c$ and $\frac{1}{a+b} + \frac{1}{b+c} + \frac{1}{c+a}$ have the same sign.