Question: Solve: \dfrac{\sqrt{x+4} + \sqrt{2} }{ \sqrt{x +4} - \sqrt{2}} = 2

Solution:
Given,

\dfrac{\sqrt{x+4} + \sqrt{2} }{ \sqrt{x +4} - \sqrt{2}} = 2

or, \sqrt{x+4} + \sqrt{2}  = 2(  \sqrt{x +4} - \sqrt{2})

or, \sqrt{x+4} + \sqrt{2} = 2 \sqrt{x +4} - 2\ sqrt{2})

or, 2\sqrt{2} + \sqrt{2} = 2\sqrt{x +4} - \sqrt{x +4}

or, 3\sqrt{2} = \sqrt{x +4}

or, \sqrt{x +4} = 3\sqrt{2}

squaring both sides

or, (\sqrt{x+4})² = (3\sqrt{2})²

or, x +4 = 9×2

or, x +4 = 18

or, x = 18-4

\therefore x = 14
= Answer