Track / Stage 4 / 311 of 340 #571 of 2000

Problem 571

AMC 12 late, AIME early

Algebra Difficulty 5.0 Find the answer

2. Given $a, b, c$ are non-zero real numbers, and $a+b+c$ $=0$ . Then the value of $a\left(\frac{1}{b}+\frac{1}{c}\right)+b\left(\frac{1}{c}+\frac{1}{a}\right)+c\left(\frac{1}{a}+\frac{1}{b}\right)$ is . $\qquad$

Your answer

Official solution

2. -3

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.