`((5.624)^(3)+(4.376)^(3))/(5.624xx5.624-(5.624xx4.376)+4.376xx4.376)` is equal to

Options

A. `10`
B. `1.248`
C. `20.44`
D. `1`

Answer

To solve the expression \(\frac{(5.624)^3 + (4.376)^3}{(5.624)^2 - (5.624)(4.376) + (4.376)^2}\), we can use the identities for the sum of cubes and the quadratic form.

### Step-by-Step Solution:

1. **Identify Variables**:
Let \( a = 5.624 \) and \( b = 4.376 \).

2. **Recognize the Formulas**:
We can use the formulas:
- Sum of cubes: \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \)
- The denominator can be rewritten as \( a^2 - ab + b^2 \).

3. **Rewrite the Expression**:
The expression can be rewritten as:
\[ \frac{a^3 + b^3}{a^2 - ab + b^2} = \frac{(a + b)(a^2 - ab + b^2)}{a^2 - ab + b^2} \]

4. **Cancel Common Terms**:
Since \( a^2 - ab + b^2 \) is in both the numerator and the denominator, we can cancel it out (as long as it is not zero):
\[ = a + b \]

5. **Calculate \( a + b \)**:
Now, substitute back the values of \( a \) and \( b \):
\[ a + b = 5.624 + 4.376 = 10 \]

6. **Final Answer**:
Therefore, the value of the original expression is:
\[ \boxed{10} \]