Evaluate:
`(5.67 xx 5.67 xx 5.67 + 4.33 xx 4.33 xx 4.33)/(5.67 xx 5.67 - 5.67 xx 4.33 + 4.33 xx 4.33)`

Answer

To evaluate the expression

\[ \frac{(5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33)}{(5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33)}, \]

we can follow these steps:

### Step 1: Define Variables
Let \( a = 5.67 \) and \( b = 4.33 \). This allows us to rewrite the expression in terms of \( a \) and \( b \).

### Step 2: Rewrite the Expression
The expression can be rewritten as:

\[ \frac{(a^3 + b^3)}{(a^2 - ab + b^2)}. \]

### Step 3: Apply the Identity for \( a^3 + b^3 \)
We know from algebra that:

\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2). \]

Using this identity, we can substitute \( a^3 + b^3 \) in our expression:

\[ \frac{(a + b)(a^2 - ab + b^2)}{(a^2 - ab + b^2)}. \]

### Step 4: Simplify the Expression
Since \( a^2 - ab + b^2 \) appears in both the numerator and the denominator, we can cancel it out (as long as it is not equal to zero):

\[ a + b. \]

### Step 5: Calculate \( a + b \)
Now we need to calculate \( a + b \):

\[ a + b = 5.67 + 4.33. \]

### Step 6: Perform the Addition
Calculating \( 5.67 + 4.33 \):

- Add the whole numbers: \( 5 + 4 = 9 \).
- Add the decimal parts: \( 0.67 + 0.33 = 1.00 \).
- Combine: \( 9 + 1 = 10 \).

### Final Answer
Thus, the final answer is:

\[ \boxed{10}. \]

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