Help Solving This?

1. √x+4 = √x-1+1

2.2√n + 3 = n
5
Rational Exponet Equations:

1.3x^5/2 - 9 = 0

2.(2x+3)^1/4=4

1. I will assume you meant

√(x+4) = √(x-1) + 1

square both sides

x+4 = x-1 + 2√(x-1) + 1
2 = √(x-1)
square once more
4 = x-1
x = 5

Check:
LS = √9 = 3
RS = √4 + 1 = 3

so x=5

#2, do it the same way after changing it to
2√n = n-3
4n = n^2 - 6n + 9
n^2 - 10n +9 = 0
(n-1)(n-9) = 0
n = 1 or n = 9

check:
if n=1
LS = 2√1 +3 = 5
RS = √1 = 1 ≠ LS

if n=9
LS = 2√9 + 3 = 9
RS = 9

so x = 9

notice after squaring, it is necessary to check all answers.

second part:
3x^(5/2) = 9
x^(5/2) = 3
x = 3^(2/5) or appr 1.552

check:
LS = 3(1.552)^2.5 - 9
= 3(3.0007...) - 9
= .00223..
= close enough to 0

you try the last one