The value of `1/2 [(0.96 xx 0.96 xx 0.96 + 0.84 xx 0.84 xx 0.84)/(0.96 xx 0.96 -0.96 xx 0.84 +0.84 xx0.84)]` is.

Answer

To solve the expression \( \frac{1}{2} \left[ \frac{0.96^3 + 0.84^3}{0.96^2 - 0.96 \cdot 0.84 + 0.84^2} \right] \), we can follow these steps:

### Step 1: Define Variables
Let \( A = 0.96 \) and \( B = 0.84 \). This simplifies our expression.

### Step 2: Rewrite the Expression
The expression can now be rewritten as:
\[ \frac{1}{2} \left[ \frac{A^3 + B^3}{A^2 - AB + B^2} \right] \]

### Step 3: Use the Formula for Sum of Cubes
Recall the formula for the sum of cubes:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]
Using this, we can substitute \( A^3 + B^3 \) in our expression:
\[ \frac{1}{2} \left[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 - AB + B^2} \right] \]

### Step 4: Simplify the Expression
The \( A^2 - AB + B^2 \) terms cancel out:
\[ \frac{1}{2} (A + B) \]

### Step 5: Calculate \( A + B \)
Now we need to find \( A + B \):
\[ A + B = 0.96 + 0.84 = 1.80 \]

### Step 6: Final Calculation
Now substitute back into the expression:
\[ \frac{1}{2} (1.80) = 0.90 \]

### Conclusion
Thus, the value of the original expression is:
\[ \boxed{0.90} \]