If sum of two numbers be a and their product is b, then the sum of their reciprocals is

Options

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

Answer

To solve the problem step by step, we need to find the sum of the reciprocals of two numbers given their sum and product.

### Step-by-Step Solution:

1. **Define the Variables:**
Let the two numbers be \( x \) and \( y \). According to the problem, we have:
- The sum of the numbers: \( x + y = a \)
- The product of the numbers: \( x \cdot y = b \)

2. **Write the Expression for the Sum of Reciprocals:**
The sum of the reciprocals of the two numbers can be expressed as:
\[ \frac{1}{x} + \frac{1}{y} \]

3. **Combine the Reciprocals:**
To combine the fractions, we need a common denominator, which is \( xy \):
\[ \frac{1}{x} + \frac{1}{y} = \frac{y}{xy} + \frac{x}{xy} = \frac{x + y}{xy} \]

4. **Substitute the Known Values:**
We know from our definitions that:
- \( x + y = a \)
- \( xy = b \)

Therefore, we can substitute these values into the expression:
\[ \frac{x + y}{xy} = \frac{a}{b} \]

5. **Final Result:**
Thus, the sum of the reciprocals of the two numbers is:
\[ \frac{a}{b} \]

### Conclusion:
The sum of the reciprocals of the two numbers, given their sum \( a \) and product \( b \), is \( \frac{a}{b} \).

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