Rationalize the denominator.
$\frac{6}{\sqrt5+\sqrt3}$

Verified step by step guidance

1. Identify the expression that needs rationalization: \( \frac{6}{\sqrt{5} + \sqrt{3}} \). The goal is to eliminate the square roots in the denominator.
2. Multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of \( \sqrt{5} + \sqrt{3} \) is \( \sqrt{5} - \sqrt{3} \).
3. Write the expression as: \( \frac{6}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} \).
4. Simplify the denominator using the difference of squares formula: \((a + b)(a - b) = a^2 - b^2\). Here, \(a = \sqrt{5}\) and \(b = \sqrt{3}\), so the denominator becomes \(5 - 3\).
5. Simplify the expression by multiplying the numerators and the denominators separately, and then simplify the resulting expression.