Question 143830
Given: {{{((sqrt(x+1) + sqrt(x-1)) )/ ((sqrt(x+1) -sqrt(x-1)))=3}}}
{{{((sqrt(x+1) + sqrt(x-1)) (sqrt(x+1) +sqrt(x-1)) )/ ((sqrt(x+1) -sqrt(x-1)) (sqrt(x+1) +sqrt(x-1)))=3}}}

{{{((sqrt(x+1) + sqrt(x-1)) (sqrt(x+1) +sqrt(x-1)) )/ ((x+1) - (x-1))=3}}}

{{{((sqrt(x+1) + sqrt(x-1)) (sqrt(x+1) +sqrt(x-1)) )/ 2 =3}}}

{{{((sqrt(x+1) + sqrt(x-1)) (sqrt(x+1) +sqrt(x-1)) ) = 6 }}}
{{{ ((x+1) + 2*sqrt(x-1)sqrt(x+1) + (x-1)) = 6 }}}


{{{ 2x + 2*sqrt(x-1)sqrt(x+1) = 6 }}}

{{{ sqrt(x-1)sqrt(x+1) = 3 - x }}}

{{{ sqrt(x^2-1) = 3 - x }}}

{{{ sqrt(x^2-1)^2 = (3 - x)^2 }}}
{{{ x^2 -1 = 9 -6x + x^2 }}}
{{{ -10 = -6x }}}
{{{ 5/3 = x }}}

Try that!