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 evaluate 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. **Multiply the fractions**:
\[ \frac{a}{b^2} \times \frac{b}{a^2} = \frac{a \cdot b}{b^2 \cdot a^2} \]

2. **Simplify the expression**:
\[ = \frac{ab}{b^2a^2} = \frac{1}{ab} \]
(Here, \( a \) in the numerator cancels with one \( a \) in the denominator, and one \( b \) in the numerator cancels with one \( b \) in the denominator.)

3. **Express as the sum of two identical terms**:
We want to express \( \frac{1}{ab} \) as the sum of two identical terms. We can do this by writing:
\[ \frac{1}{ab} = \frac{1}{2ab} + \frac{1}{2ab} \]

### Final Answer:
Thus, the product \( \frac{a}{b^2} \times \frac{b}{a^2} \) expressed as the sum of two identical terms is:
\[ \frac{1}{2ab} + \frac{1}{2ab} \]