If x = `sqrt(3)- sqrt(2)` find the value of
`x+(1)/(x)`

Answer

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

### Step 1: Write down the expression
We start with the expression:
\[ x + \frac{1}{x} \]
Substituting the value of \( x \):
\[ x + \frac{1}{x} = \left(\sqrt{3} - \sqrt{2}\right) + \frac{1}{\sqrt{3} - \sqrt{2}} \]

### Step 2: Simplify \( \frac{1}{x} \)
To simplify \( \frac{1}{\sqrt{3} - \sqrt{2}} \), we will rationalize the denominator. We multiply the numerator and denominator by the conjugate of the denominator, which is \( \sqrt{3} + \sqrt{2} \):
\[ \frac{1}{\sqrt{3} - \sqrt{2}} \cdot \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}} = \frac{\sqrt{3} + \sqrt{2}}{(\sqrt{3})^2 - (\sqrt{2})^2} \]
Calculating the denominator:
\[ (\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1 \]
So,
\[ \frac{1}{\sqrt{3} - \sqrt{2}} = \sqrt{3} + \sqrt{2} \]

### Step 3: Combine the expressions
Now substitute back into the expression for \( x + \frac{1}{x} \):
\[ x + \frac{1}{x} = \left(\sqrt{3} - \sqrt{2}\right) + \left(\sqrt{3} + \sqrt{2}\right) \]
Combine like terms:
\[ = \sqrt{3} - \sqrt{2} + \sqrt{3} + \sqrt{2} = 2\sqrt{3} \]

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