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

Explanation

To solve the problem where \( x = \frac{1}{\sqrt{3} + \sqrt{2}} \) and we need to find \( \frac{1}{x} \), we can follow these steps:

### Step 1: Write down the expression for \( x \)
Given:
\[ x = \frac{1}{\sqrt{3} + \sqrt{2}} \]

### Step 2: Find \( \frac{1}{x} \)
To find \( \frac{1}{x} \), we can take the reciprocal of \( x \):
\[ \frac{1}{x} = \sqrt{3} + \sqrt{2} \]

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

### Step 4: Simplify the denominator
Using the difference of squares:
\[ (\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2}) = 3 - 2 = 1 \]
Thus, we have:
\[ x = \sqrt{3} - \sqrt{2} \]

### Step 5: Find \( \frac{1}{x} \) again
Now substituting back, we find:
\[ \frac{1}{x} = \frac{1}{\sqrt{3} - \sqrt{2}} \]

### Step 6: 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 Answer
Thus, the value of \( \frac{1}{x} \) is:
\[ \frac{1}{x} = \sqrt{3} + \sqrt{2} \]

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