Rationlise the denominator and simplify:
` (2)/(sqrt5+ sqrt3)`

Answer

To rationalize the denominator and simplify the expression \( \frac{2}{\sqrt{5} + \sqrt{3}} \), follow these steps:

### Step 1: Multiply by the Conjugate
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of \( \sqrt{5} + \sqrt{3} \) is \( \sqrt{5} - \sqrt{3} \).

\[ \frac{2}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} \]

### Step 2: Apply the Multiplication
Now, we multiply the numerators and the denominators:

\[ = \frac{2(\sqrt{5} - \sqrt{3})}{(\sqrt{5} + \sqrt{3})(\sqrt{5} - \sqrt{3})} \]

### Step 3: Simplify the Denominator
Using the difference of squares formula \( (a + b)(a - b) = a^2 - b^2 \):

\[ = \frac{2(\sqrt{5} - \sqrt{3})}{(\sqrt{5})^2 - (\sqrt{3})^2} \]

Calculating the squares:

\[ = \frac{2(\sqrt{5} - \sqrt{3})}{5 - 3} \]

### Step 4: Simplify Further
Now, simplify the denominator:

\[ = \frac{2(\sqrt{5} - \sqrt{3})}{2} \]

### Step 5: Cancel the Common Factor
The 2 in the numerator and denominator cancels out:

\[ = \sqrt{5} - \sqrt{3} \]

### Final Result
Thus, the simplified expression is:

\[ \sqrt{5} - \sqrt{3} \]

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