Question

sqrt(2x+1)-sqrt(2x-1)=1

Answer 1

you need to square both sides

(sqrt(2x+1)-sqrt(2x-1))^2=1^2
or
(sqrt(2x+1)-sqrt(2x-1) (sqrt(2x+1)-sqrt(2x-1)=1

use foil
F=(sqrt(2x+1)(sqrt(2x+1)=2x+1
O=(sqrt(2x-1)(sqrt(2x+1)
I=-(sqrt(2x-1)(sqrt(2x+1)
L=-sqrt(2x-1) -sqrt(2x-1) =2x-1

combine like terms

4x-2(sqrt(2x-1)(sqrt(2x+1)

4x-2sqrt(4x^2-1)=1 isolate the sqrt root
-2sqrt(4x^2-1)=1-4x square both sides again
4(4x^2)-1=(1-4x)^2

Answer 2

now multiply out the square on right and multiply terms on left

you should get it from here

if not ask

Answer 3

Got it thanks!