+1072 Let a, b, and c, be nonzero real numbers such that a+b+c=0. Compute the value of 
+658 Hello SpongeBobRules24!
Distribute:
(1) \(\frac{a}{b}+\frac{a}{c}+\frac{b}{a}+\frac{b}{c}+\frac{c}{a}+\frac{c}{b}\)
Combine like terms (fractions with the same denominator):
(1) \(\frac{b+c}{a}+\frac{a+c}{b}+\frac{a+b}{c}\)
Consider:
It was given that
(2) \(a+b+c=0\)
We solve for the numerators of the three fractions in (1).
Solving:
Let us do the fraction with \(a\) as the denominator.
\(b+c=-a\)
We substitute this into (1):
\(\frac{-a}{a}=-1\)
Our equation is now:
\(-1+\frac{a+c}{b}+\frac{a+b}{c}\)
We repeat the process of solving for the numerators of the fractions in (1) and eventually get:
\(-1+-1+-1\)
Which evaluates to \(\boxed{-3}\)
