`(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))+(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))` is equal to :

Options

A. `12`
B. `6sqrt(35)`
C. `6`
D. `2sqrt(35)`

Answer

To solve the expression \((\sqrt{7}-\sqrt{5})/(\sqrt{7}+\sqrt{5}) + (\sqrt{7}+\sqrt{5})/(\sqrt{7}-\sqrt{5})\), we can follow these steps:

### Step 1: Identify the Expression
We start with the expression:
\[ \frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}} + \frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}} \]

### Step 2: Find a Common Denominator
The common denominator for the two fractions is \((\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5})\). Thus, we rewrite the expression:
\[ \frac{(\sqrt{7}-\sqrt{5})^2 + (\sqrt{7}+\sqrt{5})^2}{(\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5})} \]

### Step 3: Expand the Numerator
Now we need to expand the numerator:
1. \((\sqrt{7}-\sqrt{5})^2 = 7 - 2\sqrt{7}\sqrt{5} + 5 = 12 - 2\sqrt{35}\)
2. \((\sqrt{7}+\sqrt{5})^2 = 7 + 2\sqrt{7}\sqrt{5} + 5 = 12 + 2\sqrt{35}\)

Adding these two results:
\[ (12 - 2\sqrt{35}) + (12 + 2\sqrt{35}) = 24 \]

### Step 4: Expand the Denominator
Next, we expand the denominator:
\[ (\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5}) = 7 - 5 = 2 \]

### Step 5: Combine the Results
Now we can combine the results from the numerator and the denominator:
\[ \frac{24}{2} = 12 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{12} \]