`(3.25xx3.25+1.75xx1.75-2xx3.25xx1.75)/(3.25xx3.25-1.75xx1.75)` is

Options

A. `0.5`
B. `0.4`
C. `0.3`
D. `0.2`

Answer

To solve the expression \((3.25 \times 3.25 + 1.75 \times 1.75 - 2 \times 3.25 \times 1.75) / (3.25 \times 3.25 - 1.75 \times 1.75)\), we can simplify it step by step.

### Step 1: Assign Variables
Let \( a = 3.25 \) and \( b = 1.75 \). This will make our calculations easier.

### Step 2: Rewrite the Expression
The expression can be rewritten using \( a \) and \( b \):
\[ \frac{(a^2 + b^2 - 2ab)}{(a^2 - b^2)} \]

### Step 3: Recognize Patterns
Notice that:
- The numerator \( a^2 + b^2 - 2ab \) can be factored as \( (a - b)^2 \).
- The denominator \( a^2 - b^2 \) can be factored as \( (a - b)(a + b) \).

### Step 4: Substitute the Factored Forms
Now we can substitute these factored forms into the expression:
\[ \frac{(a - b)^2}{(a - b)(a + b)} \]

### Step 5: Simplify the Expression
We can cancel \( (a - b) \) from the numerator and the denominator (assuming \( a \neq b \)):
\[ \frac{(a - b)}{(a + b)} \]

### Step 6: Substitute Back the Values of \( a \) and \( b \)
Now substitute back the values of \( a \) and \( b \):
\[ \frac{(3.25 - 1.75)}{(3.25 + 1.75)} = \frac{1.5}{5} \]

### Step 7: Final Calculation
Now, perform the division:
\[ \frac{1.5}{5} = 0.3 \]

### Final Answer
The value of the expression is \( 0.3 \).

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