Question 34856
  sqrt(3x+1) = sqrt(x)
Square both sides of the equation to get:
3x+1=x
2x+1=0
x=-1/2
This looks like a solution but it is not.
Why?
If you substitute this back into the original equation 
you get sqrt(5/2)= sqrt(-1/2), which is not true.
Why did this happen.
When you squared both sides you introduced a solution 
which was extraneous to the original problem.
You original problem has NO SOLUTION.
Cheers,
Stan H.