Rationalize the denominator.
$\frac{5}{\sqrt3-1}$

Verified step by step guidance

1. Identify the expression that needs rationalization: \( \frac{5}{\sqrt{3} - 1} \). The goal is to eliminate the square root from the denominator.
2. To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of \( \sqrt{3} - 1 \) is \( \sqrt{3} + 1 \).
3. Set up the multiplication: \( \frac{5}{\sqrt{3} - 1} \times \frac{\sqrt{3} + 1}{\sqrt{3} + 1} \). This is equivalent to multiplying by 1, so it does not change the value of the expression.
4. Multiply the numerators: \( 5 \times (\sqrt{3} + 1) = 5\sqrt{3} + 5 \).
5. Multiply the denominators using the difference of squares formula: \((\sqrt{3} - 1)(\sqrt{3} + 1) = (\sqrt{3})^2 - 1^2 = 3 - 1 = 2\).