Hi

First you have to define the values of x for which √(2x-1) and √(x+3) are defined : [1/2 , +oo[

Then

√(2x-1) - √(x+3) = 1

√(2x-1) = 1 - √(x+3)

Square

2x-1 = x+4 - 2√(x+3)

x-5 = 2√(x+3)

Square

(x-5)² = 4(x+3)

x²-14x+13=0

(x-1)(x-13)=0

x=1 or x=13

You have now to verify by substituting the two values in the equation (because all the previous equations are not equivalent)

x=1 is not a solution

x=13 is a solution, it is the only one