`(47.53xx47.53+2xx47.53xx42.47+42.47xx42.47)/(38.25xx38.25+138.25xx138.25-2xx38.25xx138.25)=?`

Options

A. 0.81
B. 8.1
C. 81
D. 18

Answer

To solve the given expression step by step, we will identify the algebraic identities involved and simplify accordingly.

### Step 1: Identify the expression
The expression we need to simplify is:
\[ \frac{(47.53 \times 47.53 + 2 \times 47.53 \times 42.47 + 42.47 \times 42.47)}{(38.25 \times 38.25 + 138.25 \times 138.25 - 2 \times 38.25 \times 138.25)} \]

### Step 2: Recognize the identities
The numerator can be recognized as the expansion of the square of a binomial:
\[ A^2 + 2AB + B^2 = (A + B)^2 \]
where \( A = 47.53 \) and \( B = 42.47 \). Thus, the numerator becomes:
\[ (47.53 + 42.47)^2 \]

The denominator can be recognized as the expansion of the square of a binomial:
\[ A^2 + B^2 - 2AB = (A - B)^2 \]
where \( A = 138.25 \) and \( B = 38.25 \). Thus, the denominator becomes:
\[ (138.25 - 38.25)^2 \]

### Step 3: Simplify the numerator
Calculating the sum in the numerator:
\[ 47.53 + 42.47 = 90 \]
Thus, the numerator becomes:
\[ 90^2 = 8100 \]

### Step 4: Simplify the denominator
Calculating the difference in the denominator:
\[ 138.25 - 38.25 = 100 \]
Thus, the denominator becomes:
\[ 100^2 = 10000 \]

### Step 5: Combine the results
Now we can substitute back into the expression:
\[ \frac{8100}{10000} \]

### Step 6: Simplify the fraction
This simplifies to:
\[ \frac{81}{100} = 0.81 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{0.81} \]