`(10.3 xx 10.3 xx 10.3 +1)/(10.3 xx 10.3 - 10.3 + 1)` is equal to

Options

A. `9.3`
B. `10.3`
C. `11.3`
D. `12.3`

Answer

To solve the expression \((10.3 \times 10.3 \times 10.3 + 1)/(10.3 \times 10.3 - 10.3 + 1)\), we can use algebraic identities to simplify the calculations.

### Step-by-Step Solution:

1. **Define Variables**:
Let \( A = 10.3 \) and \( B = 1 \).

2. **Rewrite the Expression**:
The expression can be rewritten as:
\[ \frac{A^3 + B^3}{A^2 - AB + B^2} \]

3. **Apply the Algebraic Identities**:
We know from algebra that:
- \( A^3 + B^3 = (A + B)(A^2 - AB + B^2) \)
- Thus, the expression simplifies to:
\[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 - AB + B^2} \]

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

5. **Substitute Back the Values**:
Now substitute back the values of \( A \) and \( B \):
\[ A + B = 10.3 + 1 = 11.3 \]

6. **Final Result**:
Therefore, the value of the original expression is:
\[ \boxed{11.3} \]