Question 367892
{{{ sqrt( x+2) - sqrt (x-3) = 1 }}}
{{{ sqrt (x+2) = sqrt (x-3) +1 }}},
{{{x+2 = x-3+2*sqrt(x-3) + 1}}}, after squaring both sides.
{{{4 = 2*sqrt(x-3)}}}, after transposition and cancellation.
{{{2 = sqrt(x-3)}}},
4 = x-3, after squaring again, or
x = 7.  This value satisfies the original equation, so this is the final answer.