<PRE><B>Question 327716</B>
{{{sqrt(3x)-1=sqrt(2x+1)}}}
: 
Square both sides, FOIL ({{{sqrt(3x)-1)}}})({{{sqrt(3x)-1)}}})
:
3x - {{{sqrt(3x)}}} - {{{sqrt(3x)}}} + 1 = 2x + 1
:
3x - {{{2sqrt(3x)}}} + 1 = 2x + 1
:
3x - 2x + 1 - 1 = {{{2sqrt(3x)}}}
:
x = {{{2sqrt(3x)}}}
Square both sides
x^2 = 4(3x)
:
x^2 = 12x
Divide both sides by x
x = 12
:
:
Check the solution in original equation; {{{sqrt(3x)-1=sqrt(2x+1)}}}
Replace x with 12
{{{sqrt(3*12)-1=sqrt(2(12)+1)}}}
{{{sqrt(36)-1=sqrt(25)}}}
6 - 1 = 5; confirms our solution</PRE>