Question

Which is the rationalized form of the expression sqrtx/sqrtx+sqrt5

Answer 1

$\dfrac{\sqrt x}{\sqrt x + \sqrt 5}\\\\\\\\= \dfrac{\sqrt x(\sqrt x - \sqrt 5)}{(\sqrt x + \sqrt 5)(\sqrt x - \sqrt 5)}\\\\\\= \dfrac{\left(\sqrt x \right)^2 - \sqrt{5x}}{\left(\sqrt x \right)^2 - \left(\sqrt 5)^2}}$

$=\dfrac{x - \sqrt{5x}}{x -5}$