Simplify
`(2+ sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))`

Answer

To simplify the expression \((2 + \sqrt{3})/(2 - \sqrt{3}) + (2 - \sqrt{3})/(2 + \sqrt{3})\), we will follow these steps:

### Step 1: Find a common denominator
The common denominator for the two fractions is \((2 - \sqrt{3})(2 + \sqrt{3})\).

### Step 2: Rewrite the expression
We can rewrite the expression as:
\[ \frac{(2 + \sqrt{3})^2 + (2 - \sqrt{3})^2}{(2 - \sqrt{3})(2 + \sqrt{3})} \]

### Step 3: Expand the numerators
Now, we will expand the numerators:
1. For \((2 + \sqrt{3})^2\):
\[ (2 + \sqrt{3})^2 = 2^2 + 2 \cdot 2 \cdot \sqrt{3} + (\sqrt{3})^2 = 4 + 4\sqrt{3} + 3 = 7 + 4\sqrt{3} \]
2. For \((2 - \sqrt{3})^2\):
\[ (2 - \sqrt{3})^2 = 2^2 - 2 \cdot 2 \cdot \sqrt{3} + (\sqrt{3})^2 = 4 - 4\sqrt{3} + 3 = 7 - 4\sqrt{3} \]

### Step 4: Combine the expanded numerators
Now, we combine the results from Step 3:
\[ (7 + 4\sqrt{3}) + (7 - 4\sqrt{3}) = 7 + 7 + 4\sqrt{3} - 4\sqrt{3} = 14 \]

### Step 5: Simplify the denominator
Now, we simplify the denominator:
\[ (2 - \sqrt{3})(2 + \sqrt{3}) = 2^2 - (\sqrt{3})^2 = 4 - 3 = 1 \]

### Step 6: Final expression
Now we can write the final expression:
\[ \frac{14}{1} = 14 \]

Thus, the simplified expression is:
\[ \boxed{14} \]