<PRE><B>Question 213787</B>
{{{sqrt(x+1)-sqrt(x-1)}}} = 2
:
Add {{{sqrt(x-1)}}} to both sides
{{{sqrt(x+1)}}} = {{{sqrt(x-1)+2}}}
:
Square both sides, FOIL the right side
x + 1 = (x-1) + {{{4sqrt(x-1)}}} + 4
:
x + 1 = x - 1 + 4 + {{{4sqrt(x-1)}}}
:
x + 1 = x + 3 + {{{4sqrt(x-1)}}}
:
x - x + 1 - 3 = {{{4sqrt(x-1)}}}
:
-2 = {{{4sqrt(x-1)}}}
:
Square both sides
4 = 16(x - 1)
:
4 = 16x - 16
:
4 + 16 = 16x
:
20 = 16x
x = {{{20/16}}}
x = 1.25; however substitution in the original equation reveals this is not a solution. There is no solution

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