If `x=(1)/(sqrt(3)+sqrt(2))`. Then find `(1)/(x)`.

Explanation

To find \( \frac{1}{x} \) where \( x = \frac{1}{\sqrt{3} + \sqrt{2}} \), we can follow these steps:

### Step 1: Write the expression for \( \frac{1}{x} \)
Given that \( x = \frac{1}{\sqrt{3} + \sqrt{2}} \), we can express \( \frac{1}{x} \) as:
\[ \frac{1}{x} = \sqrt{3} + \sqrt{2} \]

### Step 2: Rationalize the denominator of \( x \)
To find \( \frac{1}{x} \) in a more simplified form, we can rationalize the denominator of \( x \):
\[ x = \frac{1}{\sqrt{3} + \sqrt{2}} \cdot \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}} = \frac{\sqrt{3} - \sqrt{2}}{(\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2})} \]

### Step 3: Simplify the denominator
Now, we simplify the denominator:
\[ (\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2}) = 3 - 2 = 1 \]
Thus, we have:
\[ x = \sqrt{3} - \sqrt{2} \]

### Step 4: Find \( \frac{1}{x} \)
Now that we have \( x \) simplified, we can find \( \frac{1}{x} \):
\[ \frac{1}{x} = \frac{1}{\sqrt{3} - \sqrt{2}} \]

### Step 5: Rationalize \( \frac{1}{x} \)
To rationalize \( \frac{1}{x} \):
\[ \frac{1}{x} = \frac{\sqrt{3} + \sqrt{2}}{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})} = \frac{\sqrt{3} + \sqrt{2}}{3 - 2} = \sqrt{3} + \sqrt{2} \]

### Final Result
Thus, the value of \( \frac{1}{x} \) is:
\[ \frac{1}{x} = \sqrt{3} + \sqrt{2} \]

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