Rationlise the denominator and simplify:
` ( 1)/( 2+ sqrt 3) `

Answer

To rationalize the denominator and simplify the expression \( \frac{1}{2 + \sqrt{3}} \), follow these steps:

### Step 1: Multiply by the Conjugate
We start with the expression:
\[ \frac{1}{2 + \sqrt{3}} \]
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator, which is \( 2 - \sqrt{3} \):
\[ \frac{1 \cdot (2 - \sqrt{3})}{(2 + \sqrt{3}) \cdot (2 - \sqrt{3})} \]

### Step 2: Apply the Difference of Squares Formula
Now, we simplify the denominator using the difference of squares formula \( (a + b)(a - b) = a^2 - b^2 \):
\[ (2 + \sqrt{3})(2 - \sqrt{3}) = 2^2 - (\sqrt{3})^2 \]
Calculating this gives:
\[ 4 - 3 = 1 \]

### Step 3: Simplify the Expression
Now, we can write the expression as:
\[ \frac{2 - \sqrt{3}}{1} \]
Since the denominator is 1, we can simplify this to:
\[ 2 - \sqrt{3} \]

### Final Answer
Thus, the simplified expression is:
\[ 2 - \sqrt{3} \]