If `a+b+c= 0`, then
`(c )/(a+b) + (b)/(a+c) + (a)/(b + c)`= ?

Answer

To solve the problem, we start with the given equation:

**Step 1: Understand the given condition.**
We have \( a + b + c = 0 \).

**Step 2: Rewrite the expressions.**
We need to evaluate the expression:

\[ \frac{c}{a+b} + \frac{b}{a+c} + \frac{a}{b+c} \]

Using the condition \( a + b + c = 0 \), we can express \( a + b \), \( a + c \), and \( b + c \) in terms of \( c \), \( b \), and \( a \) respectively:

- \( a + b = -c \)
- \( a + c = -b \)
- \( b + c = -a \)

**Step 3: Substitute these values into the expression.**
Now we substitute these values into the expression:

\[ \frac{c}{-c} + \frac{b}{-b} + \frac{a}{-a} \]

**Step 4: Simplify each term.**
This simplifies to:

\[ -1 + (-1) + (-1) \]

**Step 5: Combine the results.**
Adding these together gives:

\[ -1 - 1 - 1 = -3 \]

Thus, the final result is:

\[ \frac{c}{a+b} + \frac{b}{a+c} + \frac{a}{b+c} = -3 \]

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