<PRE><B>Question 420909</B>
{{{sqrt (X+2) - sqrt (X-3) = sqrt (X-6)}}}
;
square both sides
{{{(sqrt (X+2) - sqrt (X-3))^2 = (sqrt (X-6))^2}}}
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FOIL the Left side
(x+2) - {{{sqrt((x+2)*(x-3)) - sqrt((x+2)*(x-3))}}} + (x-3) = (x-6)
:
Combine like terms, move the radical to right
x + x -x + 2 - 3 + 6 = {{{2sqrt((x+2)*(x-3))}}}
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FOIL inside the radical 
x + 5 = {{{2sqrt(x^2 - x - 6)}}}
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square both sides
x^2 + 10x + 25 = 4(x^2 - x - 6)
x^2 + 10x + 25 = 4x^2 - 4x - 24
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Combine like terms on the right
0 = 4x^2 - x^2 - 4x - 10x - 24 - 25
:
3x^2 - 14x - 49 = 0
Factors to
(3x + 7)(x - 7) = 0
positive solution is all want here
x = + 7
:
:
Check solution in the original equation
{{{sqrt (7+2) - sqrt (7-3) = sqrt (7-6)}}}
you can see that it checks out</PRE>