Equations with radical equations Algebra 2

√x + 4 = √ x - 1 + 1

√x + 4 = √x - 1 + 1
√x + 4 = √x
4 = 0, which is false so there is no solution

If you meant √(x + 4) = √(x - 1) + 1, then
(√(x + 4))^2 = (√(x - 1) + 1)^2
x + 4 = x - 1 + 2√(x - 1) + 1
4 = 2√(x - 1)
2 = √(x - 1)
4 = x - 1
x = 5

Could you use parentheses to show us the proper groupings of what is under the √ sign

you have written √x + 4 = √x - 1 + 1
The right had side of the equation simplifies into √x

you are left with √x + 4 = √x which is never true.