If `x+y=25` and `xy=35`, then `1//x+1//y`= ?

Options

A. `57--sqrt'''57`
B. `7//5`
C. `5//7`
D. `75--sqrt'''75`

Answer

To solve the problem, we need to find the value of \( \frac{1}{x} + \frac{1}{y} \) given that \( x + y = 25 \) and \( xy = 35 \).

### Step-by-Step Solution:

1. **Start with the given equations:**
- \( x + y = 25 \) (Equation 1)
- \( xy = 35 \) (Equation 2)

2. **Use the formula for the sum of reciprocals:**
The sum of the reciprocals of \( x \) and \( y \) can be expressed as:
\[ \frac{1}{x} + \frac{1}{y} = \frac{y + x}{xy} \]

3. **Substitute the values from the equations:**
From Equation 1, we know \( x + y = 25 \).
From Equation 2, we know \( xy = 35 \).

Therefore, we can substitute these values into the formula:
\[ \frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy} = \frac{25}{35} \]

4. **Simplify the fraction:**
To simplify \( \frac{25}{35} \), we can divide both the numerator and the denominator by their greatest common divisor, which is 5:
\[ \frac{25 \div 5}{35 \div 5} = \frac{5}{7} \]

5. **Final Result:**
Thus, the value of \( \frac{1}{x} + \frac{1}{y} \) is:
\[ \frac{1}{x} + \frac{1}{y} = \frac{5}{7} \]