Question: Solve: \dfrac{\sqrt{x} + \sqrt{7}}{\sqrt{x} - \sqrt{7}} = 3


Solution:
Given,

\dfrac{\sqrt{x} + \sqrt{7}}{\sqrt{x} - \sqrt{7}} = 3

or, \sqrt{x} - \sqrt{7} = 3(\sqrt{x} - \sqrt{7})

or, \sqrt{x} - \sqrt{7}= 3\sqrt{x} - 3\sqrt{7}

or, 3\sqrt{7} + \sqrt{7} = 3\sqrt{x} - \sqrt{x}

or, 4\sqrt{7} = 2\sqrt{x}

or, 2\sqrt{x} = 4\sqrt{7}

or, \sqrt{x} = \dfrac{4\sqrt{7}}{2}

or, \sqrt{x} = 2\sqrt{7}

[ Squaring both sides ]

or, (\sqrt{x})^2 = (2\sqrt{7})^2

or, x = 4 * 7

\therefore x = 28
= Answer