The product `a/(b^2) xx b/(a^2)` expressed as the sum of two identical terms is :

Options

A. `1/(a + b) + 1/(a +b)`
B. `a/b + a/b`
C. `b/a + b/a`
D. `1/(2ab) + 1/(2ab)`

Answer

To solve the problem, we need to simplify the expression \( \frac{a}{b^2} \times \frac{b}{a^2} \) and express it as the sum of two identical terms.

### Step-by-Step Solution:

1. **Write down the expression**:
\[ \frac{a}{b^2} \times \frac{b}{a^2} \]

2. **Multiply the fractions**:
When multiplying fractions, we multiply the numerators together and the denominators together:
\[ = \frac{a \times b}{b^2 \times a^2} \]

3. **Simplify the expression**:
We can simplify the numerator and the denominator:
\[ = \frac{ab}{b^2a^2} \]
Here, we can cancel one \( a \) from the numerator with one \( a \) from the denominator, and one \( b \) from the numerator with one \( b \) from the denominator:
\[ = \frac{1}{ab} \]

4. **Express as a sum of two identical terms**:
We need to express \( \frac{1}{ab} \) as the sum of two identical terms. We can do this by writing:
\[ \frac{1}{ab} = \frac{1}{2} \cdot \frac{2}{ab} \]
This can be expressed as:
\[ = \frac{1}{2ab} + \frac{1}{2ab} \]
Thus, we have:
\[ = \frac{1}{2a} + \frac{1}{2b} \]

5. **Final expression**:
Therefore, the expression \( \frac{a}{b^2} \times \frac{b}{a^2} \) expressed as the sum of two identical terms is:
\[ \frac{1}{2ab} + \frac{1}{2ab} \]

### Conclusion:
The correct answer is:
\[ \frac{1}{2ab} + \frac{1}{2ab} \]