Simplify : `(0.0347 xx 0.0347 xx 0.0347 + (0.9653)^(3))/((0.0347)^(2) - (0.0347) (0.9653) + (0.9653)^(2))`

Options

A. 0.9306
B. 1.0009
C. `1.0050`
D. 1

Answer

To simplify the expression

\[ \frac{(0.0347 \times 0.0347 \times 0.0347) + (0.9653)^3}{(0.0347)^2 - (0.0347)(0.9653) + (0.9653)^2} \]

we can follow these steps:

### Step 1: Define Variables
Let \( A = 0.0347 \) and \( B = 0.9653 \).

### Step 2: Rewrite the Expression
The expression can be rewritten using \( A \) and \( B \):

\[ \frac{A^3 + B^3}{A^2 - AB + B^2} \]

### Step 3: Apply the Formula for Sum of Cubes
Recall the formula for the sum of cubes:

\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]

### Step 4: Substitute the Formula
Using this formula, we can substitute into the expression:

\[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 - AB + B^2} \]

### Step 5: 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):

\[ A + B \]

### Step 6: Calculate \( A + B \)
Now we need to calculate \( A + B \):

\[ A + B = 0.0347 + 0.9653 \]

### Step 7: Perform the Addition
Adding the two values:

\[ 0.0347 + 0.9653 = 1.0000 \]

### Final Answer
Thus, the simplified value of the expression is:

\[ \boxed{1} \]