`((3.537-0.948)^(2)+(3.537+0.948)^(2))/((3.537)^(2)+(.948)^(2))=?`

Options

A. 4.485
B. 2.589
C. 4
D. 2

Explanation

To solve the expression \(\frac{(3.537 - 0.948)^2 + (3.537 + 0.948)^2}{(3.537)^2 + (0.948)^2}\), we can simplify it step by step.

### Step 1: Identify A and B
Let:
- \( A = 3.537 \)
- \( B = 0.948 \)

### Step 2: Rewrite the expression
We can rewrite the expression as:
\[ \frac{(A - B)^2 + (A + B)^2}{A^2 + B^2} \]

### Step 3: Expand the numerator
Now, we will expand the numerator:
\[ (A - B)^2 = A^2 - 2AB + B^2 \]
\[ (A + B)^2 = A^2 + 2AB + B^2 \]
Adding these two expansions together:
\[ (A - B)^2 + (A + B)^2 = (A^2 - 2AB + B^2) + (A^2 + 2AB + B^2) \]
This simplifies to:
\[ 2A^2 + 2B^2 \]

### Step 4: Substitute back into the expression
Now substitute this back into the original expression:
\[ \frac{2A^2 + 2B^2}{A^2 + B^2} \]

### Step 5: Factor out the common term
Factor out 2 from the numerator:
\[ = \frac{2(A^2 + B^2)}{A^2 + B^2} \]

### Step 6: Cancel the common terms
Since \(A^2 + B^2\) is present in both the numerator and the denominator, we can cancel it out:
\[ = 2 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{2} \]