<PRE><B>Question 309847</B>
{{{sqrt(x-3) = sqrt(x+2) - 1}}}
Square both sides, FOIL the right side
x - 3 = {{{(x+2) - 1sqrt(x+2) - 1sqrt(x+2) + 1}}}
:
x - 3 = {{{x + 2 + 1 - 2sqrt(x+2)}}}
:
x - 3 = {{{x + 3 - 2sqrt(x+2)}}}
:
x - 3 - x - 3 = {{{-2sqrt(x+2)}}}
:
-6 = {{{-2sqrt(x+2)}}}
Square both sides
36 = 4(x+2)
:
36 = 4x + 8
:
36 - 8 = 4x
:
28 = 4x
x = {{{28/4}}}
x = 7
:
;
Check solution in the original equation
{{{sqrt(7-3) = sqrt(7+2) - 1}}}
{{{sqrt(4) = sqrt(9) - 1}}}
2 = 3 - 1; confirms our solution</PRE>