Question 97033
{{{sqrt(2x+3)}}} - {{{sqrt(x+1)}}} =1

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

squaring both sides of the equation we get

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

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

x + 1 = 2{{{sqrt(x+1)}}} 

squaring both sides again 

x^2 + 2x +1 = 4(x+1)
x^2 -2x -3 =0

Using {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
we have 
{{{x = (2 +- sqrt( (-2)^2-4*1*(-3) ))/(2*1) }}}
x= (2-4)/2 and (2+4)/2
x= -1 and 3