Answer
no solution
Work Step by Step
$\sqrt {x+1} - \sqrt {x-1} = 2$
$\sqrt {x+1} - \sqrt {x-1}+\sqrt {x-1} = 2+\sqrt {x-1}$
$\sqrt {x+1} = 2+\sqrt {x-1}$
$(\sqrt {x+1})^2 = (2+\sqrt {x-1})^2$
$x+1=2*2+2*\sqrt {x-1}+2*\sqrt {x-1}+\sqrt {x-1}*\sqrt {x-1}$
$x+1=4+4*\sqrt {x-1}+(x-1)$
$x+1=4+4*\sqrt {x-1}+x-1$
$1=4+4*\sqrt {x-1}-1$
$1=3+4*\sqrt {x-1}$
$-2=4*\sqrt {x-1}$
$-2/4=4*\sqrt {x-1}/4$
$-1/2=\sqrt {x-1}$
$(-1/2)^2=(\sqrt {x-1})^2$
$1/4=x-1$
$1/4+4/4=x-1+1$
$5/4=x$
$\sqrt {x+1} - \sqrt {x-1} = 2$
$\sqrt {5/4+1} - \sqrt {5/4-1} = 2$
$\sqrt {9/4} - \sqrt {1/4} = 2$
$3/2-1/2=2$
$2/2=2$
$1=2$ (false)
