Question

How do I simplify this expression?

Answer 1

We can write

$3x^{3/2}-9x^{1/2}+6x^{-1/2}=3x^{2-1/2}-9x^{1-1/2}+6x^{-1/2}$

and see that each term has a common factor of $3x^{-1/2}$; factoring this from each term gives

$3x^{3/2}-9x^{1/2}+6x^{-1/2}=3x^{-1/2}(x^2-3x+2)$

We can factorize this further:

$3x^{-1/2}(x-2)(x-1)$

This is probably what is meant by "simplify"...