[tex] \sqrt{x + 1} - \sqrt{x - 1} = \sqrt{2} \: | {( \: )}^{2} [/tex]
[tex]x + 1 - 2 \sqrt{(x + 1)(x - 1)} + x - 1 = 2[/tex]
[tex]2x - 2 \sqrt{ {x}^{2} - 1} = 2 \: | \div 2[/tex]
[tex]x - \sqrt{ {x}^{2} - 1} = 1[/tex]
[tex] - \sqrt{ {x}^{2} - 1 } = 1 - x \: | \times ( - 1)[/tex]
[tex] \sqrt{ {x}^{2} - 1} = x - 1 \: |{( \: ) }^{2} [/tex]
[tex] {x}^{2} - 1 = {x}^{2} - 2x + 1[/tex]
[tex] {x}^{2} - {x}^{2} + 2x = 1 + 1[/tex]
[tex]2x = 2[/tex]
[tex]x = \frac{2}{2} [/tex]
[tex]x = 1[/tex]
