`(1)/(sqrt(a))-(1)/(sqrt(b))=0`, then the value of `(1)/(a)+(1)/(b)` is

Options

A. `(1)/(sqrt(ab))`
B. `sqrt(ab)`
C. `(2)/(sqrt(ab))`
D. `(1)/(2sqrt(ab))`

Answer

To solve the equation \(\frac{1}{\sqrt{a}} - \frac{1}{\sqrt{b}} = 0\) and find the value of \(\frac{1}{a} + \frac{1}{b}\), we can follow these steps:

### Step 1: Set the equation to zero
Starting with the given equation:
\[ \frac{1}{\sqrt{a}} - \frac{1}{\sqrt{b}} = 0 \]

### Step 2: Rearrange the equation
We can rearrange this equation to isolate one of the fractions:
\[ \frac{1}{\sqrt{a}} = \frac{1}{\sqrt{b}} \]

### Step 3: Cross-multiply
Cross-multiplying gives us:
\[ \sqrt{b} = \sqrt{a} \]

### Step 4: Square both sides
Now, squaring both sides to eliminate the square roots:
\[ b = a \]

### Step 5: Substitute \(b\) in the expression
We need to find \(\frac{1}{a} + \frac{1}{b}\). Since \(b = a\), we can substitute \(b\) with \(a\):
\[ \frac{1}{a} + \frac{1}{b} = \frac{1}{a} + \frac{1}{a} \]

### Step 6: Combine the fractions
Combining the fractions gives:
\[ \frac{1}{a} + \frac{1}{a} = \frac{2}{a} \]

### Conclusion
Thus, the value of \(\frac{1}{a} + \frac{1}{b}\) is:
\[ \frac{2}{a} \]