√(2x-1) - √(x+3) = 1
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