We can write
[tex]3x^{3/2}-9x^{1/2}+6x^{-1/2}=3x^{2-1/2}-9x^{1-1/2}+6x^{-1/2}[/tex]
and see that each term has a common factor of [tex]3x^{-1/2}[/tex]; factoring this from each term gives
[tex]3x^{3/2}-9x^{1/2}+6x^{-1/2}=3x^{-1/2}(x^2-3x+2)[/tex]
We can factorize this further:
[tex]3x^{-1/2}(x-2)(x-1)[/tex]
This is probably what is meant by "simplify"...
