Question 1068538
√3x+1 = √x-1+2 
=> (√3x+1)^2 = 2+ sqrt (x-1)
=> 3x+1 = 4 +4 sqrt(x-1)+x-1.  I like to bring the smaller x to the side with the larger and keep it positive but one doesn't have to do that.
=2x-2=4 sqrt(x-1).  
***square both sides***remember to square the 4, too.
4x^2-8x+4=16(x-1)=16x-16
4x^2-24x+20=0
x^2-6x+5=0
(x-5)(x-1)=0
x=5 and 1
sqrt(16)-sqrt(4)=4-2=2 checks
sart(4)-sqrt(0)=2 also checks.