[tex] \frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1 } = \frac{ (\sqrt{2} - 1)( \sqrt{2} - 1) }{ (\sqrt{2} + 1)(\sqrt{2} - 1) } = \frac{ {( \sqrt{2} - 1) }^{2} }{ {( \sqrt{2} )}^{2} - {1}^{2} } = \frac{ {( \sqrt{2} - 1) }^{2} }{ 2 - 1 } = {( \sqrt{2} - 1) }^{2}[/tex]