Question

How do you solve `sqrt(x+3)-sqrt(x-1)=1`?

Answer 1

`color(green)(x=13/4 = 3 1/4)`

Explanation:

Given
`color(white)("XXX")sqrt(x+3)-sqrt(x-1)=1`

`color(white)("XXX")rarr sqrt(x+3)=1+sqrt(x-1)`

Squaring both sides:
`color(white)("XXX")cancel(x)+3=cancel(1)+2sqrt(x-1)+cancel(x)cancel(-1)`

`color(white)("XXX")rarr 2sqrt(x-1)=3`

`color(white)("XXX")rarr sqrt(x-1)=3/2`

Squaring both sides again
`color(white)("XXX")rarr x-1=9/4`

`color(white)("XXX")rarr x=13/4`