Question 208735
sqrt 2x+3 - sqrt x+1 =1 
{{{sqrt(2x+3) - sqrt(x+1) = 1}}} Is that what you meant?
If so,
{{{sqrt(2x+3) = sqrt(x+1) + 1}}}
Square both sides
{{{2x+3 = (x+1) + 2sqrt(x+1) + 1}}}
{{{x+1 = 2sqrt(x+1)}}}
Square again
{{{x^2 + 2x + 1 = 4x+4}}}
{{{x^2 -2x - 3 = 0}}}
(x-3)*(x+1) = 0
x = 3
x = -1