What is the value `[(2.4)^(3) + (0.8)^(3)] div [(2.4)^(2) +(0.8)^(2) - (2.4) xx (0.8)]` ?

Options

A. `4.2`
B. `3.2`
C. `1.6`
D. `2.2`

Answer

To solve the expression \(\frac{(2.4)^3 + (0.8)^3}{(2.4)^2 + (0.8)^2 - (2.4) \cdot (0.8)}\), we can use algebraic identities to simplify our calculations.

### Step 1: Define Variables
Let:
- \( A = 2.4 \)
- \( B = 0.8 \)

### Step 2: Rewrite the Expression
We can rewrite the expression using \( A \) and \( B \):
\[ \frac{A^3 + B^3}{A^2 + B^2 - AB} \]

### Step 3: Apply the Identity for Sum of Cubes
We know that:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]
Thus, we can substitute this into our expression:
\[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 + B^2 - AB} \]

### Step 4: Simplify the Denominator
Notice that \( A^2 - AB + B^2 \) is equal to \( A^2 + B^2 - AB \). Therefore, we can simplify the expression:
\[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 - AB + B^2} = A + B \]

### Step 5: Calculate \( A + B \)
Now, we can calculate \( A + B \):
\[ A + B = 2.4 + 0.8 = 3.2 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{3.2} \]