Start your solution by cross-multiplying, \(\frac{\sqrt{2}}{x+\sqrt{2}}=\frac{1}{x-\sqrt{2}}\) [x - \(\sqrt{2}\)]\(\sqrt{2}\) = x + \(\sqrt{2}\) where \(\sqrt{2}\) \times\(\sqrt{2}\) = 2 x\(\sqrt{2} - \sqrt{2} x \sqrt{2}\) = x + \(\sqrt{2}\) then collect like terms x\(\sqrt{2}\) - x = \(\sqrt{2}\) + 2 and factorize accordingly to get the unknown. x(\(\sqrt{2}\) - 1) = \(\sqrt{2}\) + 2 x = \(\frac{\sqrt{2}) + 2}{\sqrt{2} - 1}\) rationalize x = \(\frac{\sqrt{2} + 2}{\sqrt{2} - 1}\) * \(\frac{\sqrt{2} + 1}{\sqrt{2} + 1}\) x = \(\frac{\sqrt{4} + \sqrt{2} + 2\sqrt{2} + 2}{\sqrt{4} + \sqrt{2} - \sqrt{2} - 1}\) x = \(\frac{2 + 3\sqrt{2} + 2}{2 - 1}\) x = \(\frac{3\sqrt{2} + 4}{1}\) x = 3\(\sqrt{2}\) + 4