# How do you divide and rationalize the denominator for (x-1)/(sqrt(3x)+sqrt5)?

Mar 31, 2015

Multiply the numerator and denominator by the conjugate of the denominator

$\frac{x - 1}{\sqrt{3 x} + \sqrt{5}} \cdot \frac{\sqrt{3 x} - \sqrt{5}}{\sqrt{3 x} - \sqrt{5}}$

$= \frac{\left(x - 1\right) \left(\sqrt{3 x} - \sqrt{5}\right)}{3 x - 5}$