The value of
`[{:((0.953xx 0.953 - 0.953 xx 0.047),(" "+0.047 xx 0.047))/( (0.953 xx 0.953 xx 0.953 + 0.047),(" "xx 0.047 xx 0.047):}]` is -

Options

A. `1.5`
B. `1.00`
C. `0.87`
D. None of these

Answer

To solve the given expression step by step, we will first rewrite the expression clearly and then simplify it using algebraic identities.

### Given Expression:
\[ \frac{(0.953 \times 0.953 - 0.953 \times 0.047)}{(0.953 \times 0.953 \times 0.953 + 0.047 \times 0.047)} \]

### Step 1: Identify A and B
Let:
- \( A = 0.953 \)
- \( B = 0.047 \)

### Step 2: Rewrite the expression
The expression can be rewritten using the values of A and B:
\[ \frac{(A^2 - AB)}{(A^3 + B^2)} \]

### Step 3: Simplify the numerator
Using the identity \( A^2 - AB = A(A - B) \):
\[ A^2 - AB = A(A - B) = 0.953(0.953 - 0.047) \]
Calculating \( 0.953 - 0.047 \):
\[ 0.953 - 0.047 = 0.906 \]
Thus, the numerator becomes:
\[ 0.953 \times 0.906 \]

### Step 4: Simplify the denominator
The denominator is \( A^3 + B^2 \):
\[ A^3 = (0.953)^3 \quad \text{and} \quad B^2 = (0.047)^2 \]
Calculating \( A^3 \):
\[ 0.953^3 = 0.953 \times 0.953 \times 0.953 \]
Calculating \( B^2 \):
\[ 0.047^2 = 0.002209 \]
Thus, the denominator becomes:
\[ 0.953^3 + 0.002209 \]

### Step 5: Calculate the values
Now we need to calculate \( 0.953^3 \):
\[ 0.953^3 \approx 0.908 \]
So, the denominator is:
\[ 0.908 + 0.002209 \approx 0.910209 \]

### Step 6: Final Calculation
Now we can substitute back into our expression:
\[ \frac{0.953 \times 0.906}{0.910209} \]
Calculating the numerator:
\[ 0.953 \times 0.906 \approx 0.864618 \]
Thus, the final expression becomes:
\[ \frac{0.864618}{0.910209} \approx 0.950 \]

### Final Answer:
The value of the given expression is approximately \( 0.950 \).