Simplify : `((0.73)^(3)+(0.27)^(3))/((0.73)^(2)+(0.27)^(2)-(0.73)xx(0.27))`

Options

A. `1`
B. `0.4087`
C. `0.73`
D. `0.27`

Answer

To simplify the expression \(\frac{(0.73)^3 + (0.27)^3}{(0.73)^2 + (0.27)^2 - (0.73)(0.27)}\), we can follow these steps:

### Step 1: Identify Variables
Let \( A = 0.73 \) and \( B = 0.27 \). This allows us to rewrite the expression in terms of \( A \) and \( B \):
\[ \frac{A^3 + B^3}{A^2 + B^2 - AB} \]

### Step 2: Use the Formula for \( A^3 + B^3 \)
Recall the identity for the sum of cubes:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]
Thus, we can rewrite the numerator:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]

### Step 3: Substitute into the Expression
Now substitute this back into our expression:
\[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 + B^2 - AB} \]

### Step 4: Simplify the Denominator
Notice that the denominator \( A^2 + B^2 - AB \) can be rewritten using the identity:
\[ A^2 + B^2 - AB = A^2 - AB + B^2 \]
Thus, the expression simplifies to:
\[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 - AB + B^2} \]

### Step 5: Cancel Common Terms
Since \( A^2 - AB + B^2 \) appears in both the numerator and the denominator, we can cancel it out:
\[ A + B \]

### Step 6: Substitute Back the Values of \( A \) and \( B \)
Now substitute \( A \) and \( B \) back into the expression:
\[ A + B = 0.73 + 0.27 = 1 \]

### Final Answer
Thus, the simplified expression is:
\[ \boxed{1} \]