simplify
((1+x)1/2 - ½(1+x)-1/2) /1+X
For easier typing, let y = 1+x
then we have
(y^(1/2) - 1/(2(y^(1/2) ) ) / y
= y^(-1/2) - 1/(2y^(3/2) )
or
y^(-1/2) - (1/2) y^(-(3/2)
which could be factored:
= (1/2)y^(-3/2) ( 2y - 1)
= (1/2) (1+x)^(-3/2) ( 2x -1)
Just a lot of going round and round, not really gaining much