Answer
3
Work Step by Step
$2\sqrt {x+1}=1+\sqrt {2x+3}$
$4(x+1) = 1+ 2x+3 +2\sqrt {2x+3}$
$2x = 2\sqrt {2x+3}$
$x^2=2x+3$
(x-3)(x+1) = 0
x=3 or -1
Check the solutions to check for extraneous solutions.
x = -1 gives 0 = 2, contradiction
x=3 gives 4=4 which is a valid solution
