Given `sqrt(3)=1.7321`, find the value of the following surd, correct to three decimal places.
`(sqrt(3)+1)/(sqrt(3)-1)+(sqrt(3)-1)/(sqrt(3)+1)+(4+sqrt(3))/(4-sqrt(3))`

Answer

To solve the expression

\[ \frac{\sqrt{3}+1}{\sqrt{3}-1} + \frac{\sqrt{3}-1}{\sqrt{3}+1} + \frac{4+\sqrt{3}}{4-\sqrt{3}} \]

given that \(\sqrt{3} = 1.7321\), we will compute each part step by step.

### Step 1: Substitute the value of \(\sqrt{3}\)

Substituting \(\sqrt{3} = 1.7321\) into the expression:

\[ \frac{1.7321 + 1}{1.7321 - 1} + \frac{1.7321 - 1}{1.7321 + 1} + \frac{4 + 1.7321}{4 - 1.7321} \]

### Step 2: Calculate each term

**First Term:**

\[ \frac{1.7321 + 1}{1.7321 - 1} = \frac{2.7321}{0.7321} \]

Calculating the value:

\[ \frac{2.7321}{0.7321} \approx 3.733 \]

**Second Term:**

\[ \frac{1.7321 - 1}{1.7321 + 1} = \frac{0.7321}{2.7321} \]

Calculating the value:

\[ \frac{0.7321}{2.7321} \approx 0.268 \]

**Third Term:**

\[ \frac{4 + 1.7321}{4 - 1.7321} = \frac{5.7321}{2.2679} \]

Calculating the value:

\[ \frac{5.7321}{2.2679} \approx 2.527 \]

### Step 3: Combine all terms

Now, we will add all three results together:

\[ 3.733 + 0.268 + 2.527 \]

Calculating the total:

\[ 3.733 + 0.268 = 4.001 \]
\[ 4.001 + 2.527 = 6.528 \]

### Final Result

Thus, the value of the entire expression, correct to three decimal places, is:

\[ \boxed{6.528} \]