Question 62139
sqrt(2x+3) - sqrt(x+1) = 1, solve for x ( could be 2 solutions)

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

Square both sides:

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

Combine like terms:

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

Square both sides again:

{{{x^2+2x+1 = 4(x+1) = 4x+4}}}.

Turn this into the form of a quadratic equation:

{{{x^2 - 2x - 3 = 0 }}}.

This equation factors: {{{(x+1)(x-3)}}}.
So, {{{x = -1}}} or {{{x = 3}}}.

Let's verify these answers:

When x = -1 then {{{sqrt(2x+3) - sqrt(x+1) = sqrt(1) - sqrt(0) = 1}}}.
When x = 3 then {{{sqrt(2x+3) - sqrt(x+1) = sqrt(9) - sqrt(4) = 3 - 2 = 1}}}.