Did you watch the video?
x^2-2 equals 0, regardless whether you substitute sqrt(2) or -sqrt(2) for x.
But that is not what the video is about. The video is about algebraic expressions
that evaluate to the same result under the operation of swapping sqrt(2) and -sqrt(2)
as alternative substitutes for x.
So 1/(3+2x) is equal to (1+x)^2 if you substitute sqrt(2) for x in the first expression
and -sqrt(2) for x in the second expression and likewise if you substitute -sqrt(2)
for x in the first expression and sqrt(2) for x in the second expression.
But that doesn't mean that either of those expressions evaluates to the same
result regardless of whether you substitute sqrt(2) or -sqrt(2) for x.