If `vecA, vecB, vecC` are non-coplanar vectors then `(vecA.vecBxxvecC)/(vecCxxvecA.vecB)+(vecB.vecAxxvecC)/(vecC.vecAxxvecB)=`

Explanation

To solve the problem, we need to evaluate the expression:

\[ \frac{\vec{A} \cdot (\vec{B} \times \vec{C})}{\vec{C} \times \vec{A} \cdot \vec{B}} + \frac{\vec{B} \cdot (\vec{A} \times \vec{C})}{\vec{C} \cdot (\vec{A} \times \vec{B})} \]

### Step 1: Recognize the Scalar Triple Product
The scalar triple product of vectors \(\vec{A}, \vec{B}, \vec{C}\) is defined as:
\[ \vec{A} \cdot (\vec{B} \times \vec{C}) = \text{Volume of the parallelepiped formed by } \vec{A}, \vec{B}, \vec{C} \]

Thus, we can express the terms in the numerator as scalar triple products:
\[ \vec{A} \cdot (\vec{B} \times \vec{C}) = [\vec{A}, \vec{B}, \vec{C}] \]
\[ \vec{B} \cdot (\vec{A} \times \vec{C}) = [\vec{B}, \vec{A}, \vec{C}] \]

### Step 2: Rewrite the Expression
Now, rewrite the original expression using the scalar triple product notation:
\[ \frac{[\vec{A}, \vec{B}, \vec{C}]}{\vec{C} \times \vec{A} \cdot \vec{B}} + \frac{[\vec{B}, \vec{A}, \vec{C}]}{\vec{C} \cdot (\vec{A} \times \vec{B})} \]

### Step 3: Use Properties of Scalar Triple Products
Using the property of scalar triple products, we know:
\[ [\vec{B}, \vec{A}, \vec{C}] = -[\vec{A}, \vec{B}, \vec{C}] \]

Thus, we can rewrite the second term:
\[ \frac{[\vec{B}, \vec{A}, \vec{C}]}{\vec{C} \cdot (\vec{A} \times \vec{B})} = -\frac{[\vec{A}, \vec{B}, \vec{C}]}{\vec{C} \cdot (\vec{A} \times \vec{B})} \]

### Step 4: Combine the Terms
Now, we can combine the two terms:
\[ \frac{[\vec{A}, \vec{B}, \vec{C}]}{\vec{C} \times \vec{A} \cdot \vec{B}} - \frac{[\vec{A}, \vec{B}, \vec{C}]}{\vec{C} \cdot (\vec{A} \times \vec{B})} \]

### Step 5: Factor Out the Common Scalar Triple Product
Factoring out the common scalar triple product:
\[ [\vec{A}, \vec{B}, \vec{C}] \left( \frac{1}{\vec{C} \times \vec{A} \cdot \vec{B}} - \frac{1}{\vec{C} \cdot (\vec{A} \times \vec{B})} \right) \]

### Step 6: Simplify the Expression
Since \(\vec{C} \times \vec{A} \cdot \vec{B}\) and \(\vec{C} \cdot (\vec{A} \times \vec{B})\) are both non-zero for non-coplanar vectors, we can conclude:
\[ \frac{[\vec{A}, \vec{B}, \vec{C}]}{\vec{C} \cdot (\vec{A} \times \vec{B})} \left( \frac{\vec{C} \cdot (\vec{A} \times \vec{B}) - \vec{C} \times \vec{A} \cdot \vec{B}}{\vec{C} \times \vec{A} \cdot \vec{B} \cdot \vec{C} \cdot (\vec{A} \times \vec{B})} \right) = 0 \]

### Final Answer
Thus, the final answer is:
\[ 0 \]