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

Answer

To solve the expression given that \( a + b + c = 0 \), we need to simplify the expression step by step.

### Step 1: Rewrite the expression
The expression we need to evaluate is:
\[ \left( \frac{a+b}{c} + \frac{b+c}{a} + \frac{c+a}{b} \right) \left( \frac{c}{a+b} + \frac{b}{a+c} + \frac{a}{b+c} \right) \]

### Step 2: Substitute values using \( a + b + c = 0 \)
From the equation \( a + b + c = 0 \), we can express:
- \( a + b = -c \)
- \( b + c = -a \)
- \( c + a = -b \)

### Step 3: Substitute in the first part of the expression
Now we substitute these values into the first part of the expression:
\[ \frac{a+b}{c} = \frac{-c}{c} = -1 \]
\[ \frac{b+c}{a} = \frac{-a}{a} = -1 \]
\[ \frac{c+a}{b} = \frac{-b}{b} = -1 \]

So, the first part simplifies to:
\[ -1 - 1 - 1 = -3 \]

### Step 4: Substitute values in the second part of the expression
Now we substitute into the second part of the expression:
\[ \frac{c}{a+b} = \frac{c}{-c} = -1 \]
\[ \frac{b}{a+c} = \frac{b}{-b} = -1 \]
\[ \frac{a}{b+c} = \frac{a}{-a} = -1 \]

So, the second part simplifies to:
\[ -1 - 1 - 1 = -3 \]

### Step 5: Combine the results
Now we combine the results from both parts:
\[ (-3)(-3) = 9 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{9} \]